#geometry-and-trigonometry
1 messages · Page 346 of 1
so this is something new we are learning today and i’m still trying to understand how to go about solving this
The question is just applying those definitions, really. Have you studied the graphs of trigonometric functions yet?
not really i have the notes but no proper explanation on what i’m suppose to do this is the first day we’ve done this
i think whats really throwing me off on this equation is the numbers in the graph for some reason
Along the x-axis, that is actually pretty standard. If you Google the graphs of f(x) = sin(x) and f(x) = cos(x), you might be able to get a feel for how the graphs look and how to apply some of the terms.
hm ok i see what you’re saying!
Cool…just ping me back if you get stuck or have any questions!
ok thank you for your amazing help!!
man
do @.helpers
circles are hard im sorry ;-;
can u help with this real quick
i just wanna know if i set it up right and how i would solve that 🧍♂️
U set it up right
how would i solve it
That's what I'm trying to see
would u do 360/2 to find the base of one of the triangles
o
Ur learning trig?
yeah
okok
Alright so first u need to find the supplement of the sum of the angles of depression
huh
Do u know how to do that
noo we’re learning ab the law of sines and cosines so i think i have to use that
it’s easy but my brain is dumb so
Nah ur fine
Some people either don't get math off the bat or didn't get taught an optimal way so don't beat urself up
Anyways let's break down what I said
What are the angles of depression
the 72 and 40 degrees
so 112 degrees
It's what you get when you evaluate the root of evil 😉
Fair enough
Alright so what is a supplement @meager karma
With respect to geometry of course
i have no idea 🏃♂️🏃♂️
Oh
HAHA i don’t remember
Well a complement is an angle measure that makes another angle 90 degrees or pi/2 radians
ok then
okkkk
So now find the supplement in degrees of the sum of the angles of depression
bruh
Find the supplement of 112
68?
yes
ok how
Do u remember interior angle and alternate angles and all those
Yeah its needed here
So because we want to find how high the blimp is, we can say that the blimps height and the ground are parallel
yes
Aka the blimp is not approaching the ground or getting higher from the ground
So I want to find the rightmost angle on the big triangle
Post the hw again for me
Alright so let's say the side of the triangle that the 40 is by is infinite and is crossing both the height and the ground
Then there would be even more angles
ya so what do we do
So this is what would happen with the side
We want to find the angle with the ? by it
so alt angles for both 72 and 40
Yeah
ok
Alt int angles
so the angle on the left would be 72 and the right 40
👍
yess so now what
Now we can split the 68
So u need to find the complement of 40 and 72
Complements my bad
So the comp of 40 then the comp of 72
very nice
so which triangle do u wanna use to solve how high the blimp is
Doesn't matter
Whatever works
But let's use 40 degree triangle bc why not
Alright so do u remember the law of sines?
uhh yes
Nvm we are good
Well we have every angle we need so we can use the law of sines
To get the sides
So what angle side pair do we have
it would look like this right
Looks fine to me
Anyways there's only one angle and side that are opposite each other
uhhh
What are they?
bruh idk wouldn’t there be multiple that are opposite of each other
Nah bc there's only one side that we know of
so would it just be the 68 degrees and 360
Yep
So we want to find the hypotenuse of the 40 triangle
What angle on the big triangle is opposite to that hypotenuse
On the small triangle yes
ok
On the big triangle no
Yep
So use law of sines now
so wouldn’t that be x/sin72 and 360/sin68 or am i dumb
Man I'm excited to take trig next year with these kinds of problems
why are u excited 😭😭
Bc I've already self studied this year so I can breeze thru the class
But what did u get for x
Yep
And don't turn that into decimals
Just keep it like that
So we can be more accurate
But now it's time for the last step
wait so it’s 369.27
Yes but don't turn it into that yet
It's less accurate
so what do we do now
ok
So now we want to find the height which you can use the law of sines for
( sin(72)360 / sin(68) ) / sin 90 = x/sin(40)
Also yeah we did
The 40 triangle hypotenuse
1
Mhm
ok so what does that last step do 🏃♂️
Get the answer
Don't turn it into decimals
o
Keep it as fraction
Only turn the answer into decimals
Do u know what to do for the answer?
oh sorry there was a police man at my door LMAO
woukd it be 237.36
It sure would
No problem
I see congruence because of reflection and the sides of both triangles which I thought was -ss ; not enough info- but the correct answer was -sss congruence-. how?
the triangles share a common side
Any one willing to help me w these?
Use Gaussian Elimination can someone walk me through this
,rccw
okay so @upper karma @vast python one of you will need to move out of this channel
Oh.. why?
you posted your questions within minutes of each other
and presumably you both want help
but having that happen in one channel won't do
I’ll leave then
just go to another channel, there's no need to leave the server outright lol
okay so with this
which problem number would you like to start with?
oh but i fuigured out 9 and 10
yea
okay
the concept's the exact same here.
get the slope of your line by using its perpendicularity to the given line, and then pin down the y-intercept by using the point.
is something giving you trouble in number 7 that didn't come up in 5 or 6?
yea
okay, what is it
oh shoot nvmm i saw what i did i pinned it wrong which got me whole nother answer
well tyyy
anything else?
nope im good😀
ok
hi
i think i’m overthinking it again but can someone help me with this problem (there’s more like this but this is just one of them i don’t wanna ask for too much)
We know it goes from -pi to 3pi
So the period is 4pi
Since it goes 4 to -4 on altitude... the amp is 8/2 or 4
Btw B would be 2pi / 4pi, or 1/2
Hope that helps!
Ping me if you don’t get it por favor, and I’ll try to help
hm ok i got what you’re saying it makes total sense thank you so much!! this confuses me quite a bit you’re a really great help !!
Np
i have 2 more equations like this if it’s alright can you help me with them as well?
here they are lol
Alright, so amplitude is always (highest point - lowest point) /2...
So the first one goes from 1/2 to -1/2
A distance of 1
Divide that by 2 and you have the amp
For period, we know it goes pi/8 increments
So it’s distance is 4pi/8 when we count
And B would hypothetically be 2pi /(4pi/8)
hm ok so with the amp would it be 1/2 since we divide the distance by 2?
Yes
ok got u
Do you want to try the amp for the second one?
i can try!
What do you think it is?
i want to say it’s a decimal or fraction because of where it is located where it’s increasing
First: find the max and min values:
That would be 2 and -2
We then subtract: 2 - (-2) = 4
And the amp is 4/2 = 2
oh ok i get what you’re saying
Then, for period...
Increments of pi:
We go from 1pi to 5pi
The period would be 4pi as a result...
And B would hypothetically be 2pi/4pi = 2
Do you think you get it?
so the period in the end would be 2
No...
Have you learned the equation for these problems yet?
If not Dw about “B”
Your answer is 4pi
Nah lol, your good
It’s really confusing sometimes
You’re definitely not the only one
yeah it is lol but i get what you’re saying thank you for the help!
Np, if you have more questions, feel free to ping me
Plz,backup. before i go crazy. How do i go about calculating the angle PQR
Like we said in another channel...
you can just calculate all sides of triangle PQR and apply the law of cosines
^ that
to calculate RP hypotenuse id need an angle to work with? same for hypotenuse QP?
should i just assumed 90 degrees or what
this whole shape is a prism, is it not?
so presumably the front and right faces are both rectangles
Do you know how to solve for an angle given two sides of a triangle?
ok if thats the case, i got RP to 12.8cm and QP to 15.6cm
i know how to solve angles for 3 sides no angle and 2 sides 1 angle.
Basically, we know all the sides of the face (triangle on the top)
So use trig to find angle QR”X” on the face
do you really need that tho
Use the 180 degrees in a triangle rule to find RQ”X”
all you need is the length of RQ, which is just sqrt(12^2 + 8^2)
Aren’t we solving for an angle or something?
yeah but not the one you were talking about.
yes, angle PQR
Oh lol, my bad, I just woke up
soo assuming my calculations for RP and QP is correct. how to i find myself an angle to work with/ the last side
see here
what u do there tho? p^2=12^2+8^2-2* 12*8 *cosp?
oh, right.
after that, your angle is just $\arccos(\frac{RQ^2 + PQ^2 - RP^2}{2 \cdot RQ \cdot PQ})$
Ann
gotcha cheers, the the figure itself makes me confused xd
lets see...
it appears that your only problem is rounding when you weren't asked to
x should be 10/3, which is not equal to 3.30 exactly.
problem is 4*8 = 32 not 24
yeah im dumb lol
It’s a rhombus. There is a property of diagonals that makes the triangles solvable.
Can someone explain why e^iθ= cosθ+isinθ intuitively? I understand the proof using Taylor series but I would like a more geometric approach
I don’t if this is the correct channel to ask that
Try watching 3b1b s video it's pretty nice
It's just 2ABE use pythagoras and inverse trig it's pretty simple
Those are similar triangles in 10 since two angles between them are congruent. You can set up a proportion knowing this fact.
And 11 is an angle bisector problem where you can set up a proportion to solve for x.
Someone here can help, so you can just post your question.
anyone available?
no clearly nobody is ever available on this server which hasnt been posted to in 10 years (/massive sarcasm)
post your question.
is the formula not a^2 + b^2 = c^2?
ooh
you want the opposite of squaring.
~yes~
at least you're asking questions
Hey everyone! I'm stuck with an analytic geometry problem.
Given that VABC is a tetrahedron where AB = AC = BC = a, VA = VB = VC = b, b>a, I have to prove that (VA x VB) x VC = ( (2(b^2) - a^2 ) / 2) AB
you've written c and b in different places
Indeed, thank you.
I have used the triple product expansion formula but I am stuck at the trigonometry part of this...
is 19.03 correct? im not sure if i did it right
are those vectors or lengths
What I have so far is:
(b^2 cos(VA,VC)) VB - (b^2 cos(VB,VC)) VA
I have to prove for vectors, but the given data is for lengths
I don't know how to indicate vectors here
And I have to prove this
Sorry about the bad image quality.
can someone explain how i got the answer for X as 25.45 but it says its 18 square root 2 which is literally the same answer
can someone help me with this
very appreciated. but i dont understand where the 2 square root comes from
It comes from the same theorem
Think of it like this: a^2 + b^2 = c^2. In your case c is 10, and X takes the place of either a or b, but in this case of both, because of the 45 degree angle
This makes it 2 * a^2 = c^2
And now extract square root from both sides
Now you have square root 2 * a = c
And thus Heisenberg's answer follows
dude that's a rule
How would I solve this
what have you tried
oi
46/13= 3.538...
3.538...*5= 17.69230...
Round to the nearest 100th: 17.70
this is chemistry but anyways.
can you think of what 28% of Na, 32% of Cr and 40% of O means with respect to the mass of each component? any ideas?
@fallow ruin ^^
Can anyone help
In a 45-45-90 triangle, the Pythagorean Theorem essentially is 2(a^2) = c^2.
And since it is 45-45-90, both legs are equal length.
Tysm!
is anyone able to hop in a vc and help explain this math problem to me?
someone help me please
Use Pythagorean Theorem to solve for y.
Can someone help with university analytic geometry? I posted a problem yesterday but I'm still stuck with it
For anyone looking to help laszlow, this was his question: Hey everyone! I'm stuck with an analytic geometry problem.
Given that VABC is a tetrahedron where AB = AC = BC = a, VA = VB = VC = b, b>a, I have to prove that (VA x VB) x VC = ( (2(b^2) - a^2 ) / 2) AB
PS: I have no clue how to answer this lol. Gl
Is that a cross product?
trisecting an angle with straightedge and ruler
how do i do it for acute angles where it is possible
straightedge and ruler?
is it even possible for any acute angles
so it boils down to constructing an angle of 15 or 9 degrees respectively
well thats my issue really
is it truly a trisection to construct an angle
because if it is, 45 degree trisection is easy
simply impose an equilateral triangle onto it
trisection in the general case is impossible
so thats all you can get
like i am not even using the 45 degree angle to trisect
i am just double bisecting a 60 degree angle
Geometry pre test lol
I missed a couple weeks due to a few personal reasons and my teacher wont help me setup a date after school or sometime to catch up
do you still need help
yeah lmaoo
hah okay lol
im so stuck im trying khan academy shit dont work for me D:
do you know what is similiar triangles
what does similiar mean
do you know what is "K number" in the similiar triangles
tbh no 😓
okay lets start from what is ismiliars
so similiar triangles' chosen side's ratios are always same
and ratio is showen with K letter
yeah
ah yeah
can u say which sides are similiars in your question
okay
can you say that AB side and A1C1 sides are similiar?
no it is not, similiarity is ratio between chosen or right sides/heights
so AC and A1C1 are similiar
in similiar triangles, their angles are always same
as you can see, AB side is between 90 and 30 angle
A1C1 is between 90 and 60
so, they cant be similar sides
if you want to find k, just divide similiar sides/heights/medians etc
so AB/A1B1=AC/A1C1
ab divided by a1b1 = ac divided by a1c1?
yes, because, ab/a1b1= k which is ratio between similiar sides
AC and A1C1 are similar sides too
so their ratio will be equal to k
i think i did it a bit messy lol
oh yes lol
like, why humans write ÷ ? it looks like + and actually it is a bit different than normal divide "/"
The symbol ÷ is a fraction where the numerator and denominator are unknown (dots)
there are more difference between / and ÷
how so?
their solving order are a bit different
nobody uses ÷ outside of primary school
also you are NOT going to pull out this 6÷2(1+2) shit
@waxen glen I believe they're exactly equivalent down to how they're used
yes'nt
and yes, ÷ is less common in professional math contexts, but there are some times it could be preferable
can i use 6÷2(1+2) shit for explaining p-please
Fractions are great but you don't always want to have to break out of normal line size
then put parentheses in such a way that your expression is unambiguous.
you don't have to tell me
is the answer to this not 9? [ like (6÷2) ×(3) = 3×3 =9 ]
or is it somehow 1 because 6 ÷(2×3) =6÷6=1 for some reason
the whole point is that it's ambiguous as written.
Yes
.
.
hi, i'm pretty new here :)) i can solve this thing but it will take too long for me to type in each value. Is there any practical solution for solving this types of things?
You need to write it summation form?
there is no instruction about that but if i need to, i will... my teacher isnt that strict about methods
as long as the correct answer is given
and im still in grade 9 so i might not understand a lot of stuff :<<
consider some properties of sine
sin(x) + sin(360° - x) = 0
sin(x) + sin(180° + x) = 0
and/or the locations unit circle.
you should see that there will be a lot of cancellation
thank you :)) will update later if i struggle xD
How would you go about proving that something can be inscribed in an ellipse? Five points, foci, something else?
Fiddling with the construction can be done here: https://www.geogebra.org/geometry/ttkza5zj
Some kind of projection? A "skewed" hexagram looks like a regular hexagram seen in three dimensions from a perspective.
Maybe not, it can become quite elongated...
do circles not become ellipses when seen in 3d perspective?
I think so.
I suppose that if I can find the projection that takes an ellipse to a circle it should take each vertex point to 60 degrees apart, and then we're done, but I am not so sure that is the simplest way.
That's also given that my hunch about the perspective is right.
It reminds me of the reflection property of the orthocentre across a side
Are angle bisectors persevered under projective transformations? 🤔
Surely not
But I can by continuous movement of the point A transform that thing to a regular hexagram on geogebra, while all the bisectors remain bisectors.
No, I think trilinear coordinates may be a way forward, as mentioned here: https://en.m.wikipedia.org/wiki/Steiner_ellipse
In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its vertices) whose center is the triangle's centroid. Named after Jakob Steiner, it is an example of a circumconic. By comparison the circumcircle ...
Bashing won’t give you a vivid solution
This reminds me of the incircle-excircle lemma if you’ve seen that
I figured it out. It’s a generalisation of the 9 point circle
The same construction works for any point, the angle bisector condition is redundant
I understand the working out, but I keep getting the wrong answer. How do I put the right equation into my calculator? It keep giving me a totally different answer
That’s the answer, when I put what h equals to it’s giving my a different number
Nvm
Thanks, I’ll look into that tomorrow. Are some of the same points sufficient to determine the ellipse, or did you mean something else when you said generalization?
Yeah 9 special points are on the ellipse. Pick a point P inside the triangle. Draw the ellipse through the midpoints of AB AC and BC as well as the midpoints of AP and BP and you’ll see it passes through the midpoint of CP as well as the intersection of AP and BC, intersection of BP and AC, intersection of CP and AB
<@&286206848099549185>
@feral plank if triangle's chosen sides' ratios are same, then they are similiar
I already turned it in man dont waste ur time
is this a test 
pre test
the "1 point" thing is added up, like an actual test, but it goes to the hw category for our grade.
okay
I was wrong actually, it goes into the review category for my grade
anyway
do you still need help with this question
i know it's been like half an hour
yeah lol
sorry for the delay on my end
ok
do you know what the midsegment of a triangle is
yea
i used to be good at them but like kinda forgot the stuff bc i havent done it in so long
bruh
this is last chapters stuff
lmao
i failed the test but this should help it
i mean my grade anyway
reviews are like 30 or something %
nice question dodge
no
add each angle and it equals that distance?
lol uh i thought thats what it was
the midsegment connects the midpoints of two sides
in any case, triangles ABC and DBE are similar, with a scale factor of 2
no the answer isn't 2
just because i said the number 2 somewhere doesn't mean the answer to your problem is 2

lol welp im dumb what can i say
i was kinda confused bc u said scale factor but thats not really the thing
the type of solving its asking
i mean
one triangle is half the size of the other
oh yeah lol
i see that now
LOL how the fuck did i not see that before
oml im special
yeah that makes sense
is it just me or is the diagram over specified
the angles don't seem the match the values of the sides given that DE is the mid seg
why not? angle C could be 72 degrees, and angle EDB could be 63 degrees
and angle B = 45°
so is x 45 ?
bruh what the hell
i was not even talking to you, i was addressing ramonov's doubt about the angles
ik
how about you actually read the messages i am sending instead of plucking a number i said out of context and asking me whether that's the answer
4 234 45367 2342 2345623 324565344 6574536345 345345 3223453 464654562 345624579 454569 223463458 42069
9919299135825 32838383548 232234 01341012049 56934596394593 220342 65534
hymnth
triangle DBE is literally the same as triangle ABC but shrunk by a factor of two
idk what else to tell you
aight
if this isnt enoyugh for you to find the length of DE
then maybe you need to review similar triangles
instead of making me majorly upset like you just did
based on the length of sides, wouldn't the angles work out to be around: ||~55.7°,~41.4°, ~82.8°||
if u got upset bc im retarded ...
there was no need to call yourself a slur
if u still need help here's the explanation:
they are similar triangles and the mid segment is DE, that means CE and EB are the same and AD and DB are the same. 5+5 is 10 which is one side of the triangle ABC and 5 is the length corresponding to 10 of triangle DEB
therefore we can divide the corresponding side lengths to get the scale factor:
10/5 = 2
since we now know the scale factor is 2, then we can find x
what is the corresponding side length to x? it's AC which is given the value of 8.
the scale factor is 2, so divide 8/2 which gives you 4
x = 4
hope that helped 
thank you
no prob !!
it did
yay :))
little confusing but ill reread for the next couple to figure them out
ok if you have any questions then just @ me or something lol
yes i will tysm
VECTOR
One message removed from a suspended account.
One message removed from a suspended account.
hey if tan x= 1/3 and tan x = sin x/cos x. This means sin x = 1 and cos x = 3 right?
no
well shit
i just messed up my mid term question then
how was i suppose to tackle this if not?
draw a triangle,
apply pythagorean identities
how would i solve for z and y. ive solved for X it is 16.2 but i dont know how to solve for z and y
@vapid stag not necessarily
you have to use similar triangles
i think you also have to assume that the angle made with side x and side y is a right angle
Help?
help too? lol
The problem gives you the range of the function, which is [4, 10], and the time span it takes to reach low tide from high tide.
Knowing that high tide would be 10ft, and low tide, 4ft, you should be able to produce a wave function.
similar triangles and find the scale factor
am i able to ask questions for geometry here?
yep !
ok thanks
so basically ive been working on flow charts a bit ima send a pic of the problem
all ive really gotten written down is the basic parts like whats given
i was hoping to get some help on solving this
im rlly bad at writing proofs so um .... if u dont get a response from someone then @ the helpers tag after 15 minutes
ok thanks
find the ratio of the two right triangles
So 6/15= 0.4
And then 0.4 * 16.2: y
0.4 * 6 : z
<@&286206848099549185>
does anybody know how to
I need to prove that the triangle AEF is isosceles. DA and FX are parallel
AD is also the bisector of the angle BAC
wait I think I got it
I basically cut AD and FX with the transversal AC so DAC = AEF and then cut AD and FX with the transversal BF and BAD = BFX
no idea if it's correct though
should be
Do you still need help?
yes please!
Because of the givens, you can assume that RS is congruent to QT.
ok i got that part so far, but i was unsure of the "official" reasoning
i wrote cpctc as the reason
is that ok or should i change that?
Hm…I am not certain what you would write in the proof for that lol.
It’s been a while.
ah no worries
im a bit confused what you mean by that
Basically do you know how to prove what you need to prove besides that step.
Not really, let me grab a screen shot of what ive done so far, its really basic
sorry one second
that was my previous one
heres the newer one
So you have proven two sides of SQR and TRQ congruent.
And we know triangle PRQ is isosceles.
ah ok
Well, you’d need to document that RQ is congruent to RQ by reflexive.
ok one second
sorry how would i write that? would it just be rq is congruent to rq by reflexive or is it something else
The actual property is called the Reflexive Property of Congruence.
ok thanks
So now we have two sides of them congruent.
ok
since you know RS=QT and PS=PT would you be able to prove they are congruent from that?
You need one more thing.
ah ok
You have two sides.
PR and PQ?
Yes. There is a way to prove the angles in that larger triangle are congruent.
Angles PRQ and PQR
Im not sure of the proper way to say it but
woudlnt it be because it is an isosceles
and the bases are equal as well as the legs
Yep. The Isosceles Triangle Theorem.
Ok so I should add that onto the chart right?
Yep!
So your next statement should be about the triangles you just proved are congruent.
PRT and PQS?
No.
which ones would that be then?
This is what you have.
Yeah
Those angles are in the triangles SQP and TPQ.
Because we only know that the largest triangle is isosceles.
PRQ.
in the screen shot you sent there is p on the triangle twice, which one are you referencing
lol all good
Bottom left should be R.
It doesn’t matter what order when you talk about triangles.
Only angles order matters.
ok
I think we are good
it seems pretty simple from here I was kinda struggling with the begining
I appreciate all the help
Cool. Ping me back if you get stuck or have a question.
ok thanks!
do you have the actual diagram
Try connecting some points to create simpler figures
I believe this was given the necessary attention in one of the question channels earlier (cross-posted).
alright so i got a bit of a weird question here
it's not that i don't know the solution, i'm just blanking on how to find it without coordinate-bashing
pic incoming
ABCD is a rectangle, BD = 7, AB = 4, show that BX = 3
sick drawing
thanks i made it in 40 seconds in ms paint
similarity?
BX = 3
excellent, this fills the gap in my student's 3d geometry problem.
Does anyone know how to do proofs?
Not paragraph form. My teacher makes us do statements and reasons
@tiny snow : Is it IM that is == 5 ? or IJ ?
Do you have a specific question in mind that needs solved? You posted completed proofs, so do you just need the logic explained on those ones?
Either way, if you really don’t understand it, it might be something you want to set aside a block of time to go over with someone.
can someone please help me on this if possible
@near imp start with a diagram
i got everything figured out! except the function
can someone help me with these problems please
use sohcahtoa and sum of angles
The first one you can find angle Y easily since there are 180 degrees in a triangle. You just find the sides by using trig ratios.
Well, actually, all of the problems posted make use of trig ratios.
Except Question 2, which can be solved using an easy shortcut with Pythagorean Theorem.
i don’t believe my teacher taught us how to solve that way
oh wait nevermind i got number 2
What about law of Sine for Q2 for Q3 since it’s a 45 45 90 there is a pattern
The hyp is usually the adj side with root 2
ok i got the answer for question 2
Good.
Sry I meant for the last question in the order that it was given sry
oh don’t worry lol!
Yeah so for Q3 just use law of sine
ok i got the answer for Q3
Cool cool
and i got Q3 now i just need the first problem
i need to simplify (sin x + tan x)/(1 + sec x)
i've tried everything I can think of, I can't simplify it
i know I'm just overlooking something - I really need an answer because I couldn't find anything anywhere on the internet
Plug 5 in for d since it was five days later that it doubled. Basically, that second factor should equal 2, since the population doubled to 20,000.
In the correct choice, the second factor does simplify to 2 with the properties of exponents.
how do i solve this? i tried it 5 times with the formula my teacher gave me and it didnt work
Because those are two tangents, the measure of arc JL is double the measure of angle JKL.
You can set 2(mJKL) = mJL.
Solve for x, then the rest is straightforward.
Alright, so the problem I posted yesterday was missing two lengths, which made it have an infinite number of solutions. Here's the correct problem statement. It was supposed to be a continuation of a problem that was posted here yesterday, so it's not as well placed now as it was then.
Thank you so much 💜
I mixed up a square root... now the imaginary numbers are gone.
,w y^2+3^2-z^2=2^2, l=sqrt(33)+m-z-y, m^2+x^2=7^2,(l-sqrt(33)+y+z)/7 = z/3, (l-m+z+y)/7=y/2
So, what is the obvious solution that x = 8/3? I cannot see it...
you could do it with trig and sine rule
I see how we can find <AFE, but <DHG?
sine rule
also don't explicitly need the angles
just knowing the sine of the angles is sufficient
You mean this "sine rule"?
Radius of the circumcircle.
In order to use that you would need actual triangles, right? That have not been truncated by the square. Would you extend EF and GH to produce these, or introduce segments HE and FG?
no additional construction is needed
You'll have to give me some more info then 🙂
you can determine sin(<AFE) from triangle AFE
from that you can determine sin(<DHG) using the sine rule (in triangle FHP)
that would also be equal to x/7
and you can then determine x
Ah, now I see it. Ok, let me work it out.
Thanks @silent plank, that was much more straightforward.
Generally $x = \frac{|AE||FP|}{|HP|}$
Roenbaeck
So $\frac{|DG|}{|FP|} = \frac{|AE|}{|HP|}$ (nice ratio)
Roenbaeck
I need to calculate the TSA and V of this
I was wondering what do I do with the 135 degree angle, can I convert it to mm or is there a formula or formulas I can use it in to get a more accurate Area/volume
Does anybody have any idea on if you can write
$\frac{1}{2} ln(1 - x^2)$ in terms of inverse hyperbolic trig functions
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$\cosh\left(\tanh^{-1}{x} \right) = \frac{1}{\sqrt{1 - x^2}}$
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so
$\ln\left(\cosh\left(\tanh^{-1}{x} \right) = \frac{1}{\sqrt{1 - x^2}}\right) = - \frac{1}{2}\ln(1 - x^2)$
$\ln\left(\cosh\left(\tanh^{-1}{x} \right)\right) = - \frac{1}{2}\ln(1 - x^2)$
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so ln(cosh(atanh(x)) looks suspiciously like an inverse hyperb. trig function of its own to me
because $= -\frac{1}{2} \left( \ln(1 - x) + \ln(1 + x) \right)$
Can anyone help me...PLEASE 🥺
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If you accurately model that shape in a 3d modeling program, it can immediately give you the volume.
don't ask to ask please.. just ask your question
I know I've paid a guy on fivver to make me a 3d model. But I have to show working out on area and volume
@zenith copper I asked already
So this is a math exercise, or why do you need to show calculations?
It's an assignment
That's pure evil if you have to calculate it.
Part A is a worksheet- done that
Part B is a 3d model of a real life object along with calculations or TSA and volume showing working out
Part C is showing your research and putting together a report/ analysis
That is about 1000 words atleast
Wait, so you picked this object?
Yes becuase anything less complicated wouldn't get me an A
I need an A to get in advanced classes so a different school will take me becuase I've gone under a large amount of emotional abuse at this one and want to leave it behind
I got jumped and they gave the people a 10 minute detention. I basically go to school in the hood 😂😂
I'd ask what the least complex object that would give me A would be, while explaining the problems with the current one, then switch.
This is set in stone...
My teacher said I don't have to use the angle and just make it straight and use the height measurement for the width to get a about right answers but I'd have to compare to the one my 3d software gives me and explain why mine has a margin of error
I just want to do the angle because I want this to be perfect
Tough luck. I doubt calculations would be any more accurate than what you get from a 3d program.
So school pays some other person to do the modeling work?
I know my 3d program will give me 100% accuracy. But I want to get almost the exact same as the 3d model software gets to prove that I know my shit
I had to pay the guy...
Plus paid for the software, I've spent about $200
Why not do it yourself? There's free software, like SketchUp.
I've already gone too far. I also have no idea what I'm doing with 3d models
I've already paid the guy and brought solid works
But it sounds from the assignment that you should know 3d modeling?
It's a maths class not a 3d modelling class
They shrug and say "lol figure it out on your own lmao"
@tiny snow will you help me?
I'd split it into these parts:
A - rectangular prism minus semi-cylinder
B - triangular solid prism (x 2)
C- rectangular solid prism
D - rectangular solid prism minus 4 cylinders (x 2)
Given that I understood the drawing correctly. That'll give you simple calculations and a rough estimate.
If it's hollow you'd have to do some other division, but you get the idea.
Me and you had a preaty simmler idea
Any pointers on the other sides?
@tiny snow how do I find the measurements of A B C
A B C? Measurements are in the blueprint.
Well A has a length of 330.21mm but how do I find the width
What A? What are you doing?
Aha
For the triangles I have the hypotenuse so I just do a^2 + b^2 = c^2 right?
The blueprint is drawn to scale, so you can measure missing stuff directly and scale it appropriately.
Have to find a big peace of paper lol ight thank you for your help
can someone pls help with these two swaggy questions? thank you 🙂
Sure, I'll try. Hold on a sec
So for 1, you can first expand the whole thing into the base functions sin and cos: $\frac{\frac{1}{\cos^{2}x \cdot \frac{1}{\sinx}}{\frac{1}{\cos^{2}x + \frac{1}{\sin^{2}x}}}$.
Then you can simplify these into: $\frac{\frac{1}{\cos^{2}x \sinx}}{\frac{\sin^{2}x+cos^{2}x}{\sin^{2}xcos^{2}x}}$
Then you can simplify the numerator of the denominator to 1. $\frac{1}{cos^{2}sinx} \cdot \frac{cos^{2}xsin^{2}x}{1}$
If you simplify this, you will eventually get an answer of $sinx$.
6EQUJ5
So for 1, you can first expand the whole thing into the base functions sin and cos: $\frac{\frac{1}{\cos^{2}x \cdot \frac{1}{\sinx}}{\frac{1}{\cos^{2}x + \frac{1}{\sin^{2}x}}}$.
Then you can simplify these into: $\frac{\frac{1}{\cos^{2}x \sinx}}{\frac{\sin^{2}x+cos^{2}x}{\sin^{2}xcos^{2}x}}$
Then you can simplify the numerator of the denominator to 1. $\frac{1}{cos^{2}sinx} \cdot \frac{cos^{2}xsin^{2}x}{1}$
If you simplify this, you will eventually get an answer of $sinx$.
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wait
So for 1, you can first expand the whole thing into the base functions sin and cosine.
$\frac{\frac{1}{cos^{2}x} \cdot \frac{1}{sin x}}{\frac{1}{cos^{2}x} + \frac{1}{sin^{2}x}}$
Next, you can combine both the numerator and the denominator into one fraction.
$\frac{\frac{1}{cos^{2}x sin x}}{\frac{sin^{2}x + cos^2{x}}{cos^{2}x sin^{2}x}}$
Then you can multiply the reciprocal of the denominator times the numerator.
$\frac{1}{cos^{2}x sin x} \cdot \frac{cos^{2}x sin^{2}x}{1}$
Finally, you can simplify and eventually get the final answer of $sinx$.
For 2 you can rearrange it to get $(\sin x )^2=1/2$ so then you have two equations, $\sin x=\sqrt{2}/2$ and $\sin x=-\sqrt{2}/2$. Find the values of x in the asked interval for each, then combine both lists
thank you guys! for number two tho mikey, i don’t really know how to do the interval thing could you help with that as well
^
So this is kinda just looking at the unit circle, for the first equation find what values make sin x equal sqrt(2)/2 and do the similar thing for the second. You should find two values from each equation
You can find the height of the given right triangle
And after that use Pythagorean theorem
@earnest echo and to find the height i'd need to do 40/tan 45, or do i use special right triangles
our teacher is out on leave and we have no one to teach us this unit, we were basically on our own
45-45-90 triangle
excuse any dumb questions i make lol
How do you know that?
true
we arent given a second angle measure
so it could literally be 90 44 and 46 for example, so i shouldnt use that
👍
@upper karma Already solved, and they arent looking fo simplest radical form
"to the nearest tenth of a meter"
Thanks though ❤️
lots of people do
next time just ask your question
Ok thank you
After you get the 3rd side, remember cosx = adjacent side / hypotenuse
Yea I did cos-1(12/20) and got 53.13
Nope
You got the right side length
The adjacent side is 12. The hyponetuse is 20. Therefore, cosx =?
Uhm
the question doesn't ask you to find x, nor do you need to
Oh so the answer is just 12/20
Oh thats why I was confused
So if I have to find the measurement of c would I use tan?
yes
or use complementary angles???
wdym
👍
Steve is standing on a hill and his line of sight is 51 feet directly above the ground. He can see two deer grazing in the distance. If the angles of depression to the deer are 35° and 47° how far apart are the deer?
Okay so this is my homework question and I dont know how to even send up the triangle to this question
Have you drawn a picture of the situation?
I tried it doesnt look right

