#geometry-and-trigonometry
1 messages ยท Page 320 of 1
@mossy valve the angle J is (6x+18)ยฐ
and since it's isosceles triangle, then their basis will be equal to each other
6x+18 = 8x
that makes sense since both of the other sides are equal
they are equal
where did you get stucj?
what exactly were you solving?
Should get 16x+32=x^2+7x+10
then we subtract the left side and get x^2-9x-22
no problem
I didn't understand why we had to take a line which passes through 0,1 and r,0 . Why did we take an X intercept in the first place?
I didn't understand why we had to take a line which passes through 0,1 and r,0 . Why did we take an X intercept in the first place?
@next jackal I don't understand your question; a straight line with a y intercept of 1 should have a an x-intercept
Except for the line y=1 which does not intersect the circle at any other point
If your question is "where did this construction come from" I would recommend you read the whole proof
The aim is to find a paramteric form of Pythagorean triples
The aim is to find a paramteric form of Pythagorean triples
@lean citrus didn't we already do that by showing (a/c)^2+(b/c)^2=1?
No see that's not a parametric form
I didn't get what the number r signifies here, is it just an x intercept? or is it like an input for a side of triangle?
Yes when you construct the line, you consider r to be the x intercept
Now the goal is to express both x and y in terms of r
why in terms of r?
Well that's what we are aiming to do!
Define all possible Pythagorean triples
What we have done is derived a general form of the Pythagorean triple in terms of a single paramter
Lemme give you a simple example
"all odd numbers are of the form 2n+1, where n is an integer"
So you define all odd numbers in terms of a single parameter n. By considering different values of n we are to get different odd numbers
In a similar way, the goal here is to get a form for the Pythagorean triple in the form of a single parameter
x^2 + y^2 = 1 is a bit difficult to work with
Coz there are 2 variables
i feel like I'm not being able to clear your doubt
r is a parameter which can take any real value ,
Put value of r
You'll find different rational coordinates
Yeah I wanted to get that through to researcher
I understood that, It was meant for researcher haha
I think I'm not very good at explaining things
I want to know how we're taking more than the radius of the unit circle
What is the problem?
like any rational number, more than unit circle, how're we getting a solution for a pythagorean triple?
I'll try to go through the whole proof again
I'll try to go through the whole proof again
@next jackal good idea
I mean. When you square and add those coordinates in terms of r, you get 1
no value of x and y will be >1 for any r
it just looks like as r increases, value of y intercepting the circle increases too, but doesn't cross 1, if you take from 1,0 .
how do both increasing values add to 1?
X decreases as r increases
what? x is r right?
No?
no
See see see see see
x is (2r)/(r^2 +1)
r is a term we have assumed so that we can express both x and y in terms of r
but we take x as r in the point r,0?
r is a term we have assumed so that we can express both x and y in terms of r
@lean citrus ohhhh
but....
you derive them in those terms
but we take x as r in the point r,0?
@next jackal no... That point is not in question... We are concerned about the point of intersection of the circle, and the line between 0,1 and r,0
This particular construction allows us to express both x and y in terms of a single r
x= 2r/(r^2+1) , y= (r^2 -1)/(r^2+1) are coordinates of a point on circle, just expressed in terms of r
To repeat what Ragnarok said
PROVE: $\frac{\left(tanx+secx-1\right)}{tanx-secx+1}=\frac{\left(sinx+1\right)}{cosx}$
A pOtaTo:
could somebody help me with this?
what have you tried
could somebody help me with this?
@upper karma do you need a solution or a hint?
I like to prove such identities by simply taking the expression on the right, and multiplying and dividing it to the expression on the left
It's a bad method, but usually works
I did a little bit, wait a min. I'll send you
Yeah see whats on the right, and try to make it fit the left side, even if it doesnt look conventional
thats what i personally do too
you can use that idea like this:
LHS $= \underbrace{\frac{\tan(x)+\sec(x)-1}{\tan(x)-\sec(x)+1} \cdot \frac{\cos(x)}{\sin(x)+1}}_{\text{problem reduces to showin that this is 1}} \cdot \frac{\sin(x)+1}{\cos(x)}$
ramonov:
which would be considered more acceptable than mixing the two sides directly
Thanks @silent plank for translating t through Texit
I mean, it's a good idea to break down stuff into sin and cos
Not much helpful here tho
At least I can't intuitively rearrange this into the expression required
@silent plank mentioned this method
ohh i am getting it. Thank you
I'm sorry my handwriting is extremely bad
@lean citrus 1000000 times better than mine
๐
do you write in one flow?
like it seems like cursive without the joining lines
its really neat
meanwhile my sin looks like sn^2 x when i write it
cause i write it so quickly and mercilessly ๐
lol
I found my mistake. @lean citrus I was assuming all the points on a unit circle were rational coordinates.
(1/sqrt(2), 1/sqrt(2)) would like to have a word with you
I found my mistake. @lean citrus I was assuming all the points on a unit circle were rational coordinates.
@next jackal lol
yeah that's why I didn't get why we were doing this derivation
So if one coordinate is rational, does it mean the other has to be rational too?
okay thanks... I couldn't find one. BTW why does this book say something that seems like it's saying that?
does it?
the book simply says the construction starts with one rational point and generates more points which are distinct from the first but are still rational
okayy....
it does not say that a point on the unit circle with one rational coordinate automatically has the other coordinate also rational.
'Many more', not 'only'
okay got it
while I understand that statement on the graph, I don't understand how that fits into the equation....
$\frac{2r}{r^2 + 1} = \frac{2}{r + \frac{1}{r}}$
Ann:
as r goes to positive or negative infinity, the denominator does the same
and $\frac{r^2 - 1}{r^2 + 1} = \frac{1 - \frac{1}{r^2}}{1 + \frac{1}{r^2}}$, so as $r$ grows large $\frac{1}{r^2}$ approaches 0 and so that fraction approaches 1
Ann:
Makes sense
solve for x
We look at a solution to a nice and quick geometry problem. Inspired by this:
Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirm...
thanks man
wait a second...
He mentioned "Angle-Angle-Angle theorem"
but that is technically impossible
i mean an angle does not change if you increase the side length
length of all the sides. not just one.
So both those triangles in the corner are similar.


lol we have 3b1b emotes?
is this right
guys i need help
ok
with geometry
ok well then can someone else help ๐
how would i find the missing angles. im so confused sorry
oh boy
Can anyone help me with these two problems, I've been sick for a week and I have no idea what I'm doing.
Iโm confused
what are you confused about?
Hi, if I have a point O on acute triangle ABC, such that angles OAB = BCO and ABO = OCA how can I prove that line AO is normal to BC?
yo can someone help me out with this one
what is the smallest positive integer value of k such that sin(theta) is negative. (theta is 56 degrees)
@silent plank if you understand
@upper karma Gotta know your angle theorems
gj
ty
i think its 2y+70 = 180 @glass rover
or 110 = 180-2y
would be the same answer either way no?
oh wait no
70=180-2y
i took this math a year ago u got me confused lmao
wdym?
since its a linear pair it would be 110+2y = 180
its a supplementary angle so two angles = 180
I think you are right
I was just going off internal angles and angles whos vertices touch
@upper karma by normal do you mean perpendicular
ye
well i'm not sure how you can prove this but.
triangle ABO is equal to triangle ACO
How so?
anyone able to help me essentially walk me through this college trig course? or have the time to do so? Looking for like tutoring kind of thing idk how that works or if it is allowed etc. very behind, have no clue what's going on....class is online...sigh
you need help with sin, cos, tan?
@upper karma I'm considering that the statement doesn't necessarily need to be true
oh yea and wuf idk how to prove it, i just maed a triagnle with those angles specified
Because I was playing around and I got that angles between AO and BC (k and k') are in this relation: k - k' = a2 - b2, where a2 = BAC - BAO and b2 = angle ABC - angle OBA
So they are perpendicular if a2 = b2
That's part of it I'm not too sure where that stops and if I get into something different but for the most part I'm seeing a lot of that
@upper karma solved it
Just have to do bunch of similarity stuff
Then prove a2 = b2
And from there prove k = k'
And btw ACO and BCO are not similar unfortunately
cuz a1 != a2
but AB'O and BOA' are
is there a way of solving for x given just these details?
y is easy to find, then x is a cosine law away
Wait, but that bottom triangle is impossible haha
@surreal vector
Yeah both those triangles can't happen
oh my bad
I tried to solve it using cosine and sin
but I got that x is shorter than 30 which shouldnt be possible
why cant they happen tho?
The bottom one is a 45 degree angle, which means both sides should be the same
Similar logic on top @surreal vector
The bottom one? where do we have a 45 degrees angle here?
oh isnt the left side is just 25 - 13?
Like this, right?
which leaves me with x = 32.310
x^2 = 12^2 + 30^2
nice property? LMAO what is that?
a property is a feature that the triangle would have
do you know what it is called when a triangle have two sides of the same length?
isosceles ?
sum is always 180ยฐ , has two equal angles , two equal sides obviously
sum is always 180 degres goes for all triangles! This an important part of solving it yes.
iโm just confused on what iโm supposed to do because we literally just learned this
okay
so the triangle is isosceles then the two angels at the bottom are the same
Can you see the image I sent?
yes
okay so the third unknown angel what must it be?
well in the notes we took my teacher takes two angles and puts the like equation and equals it to another one and breaks it down to find x- i feel very dumb rn so sorry if iโm confusing -
don't worry it's fine, but I am asking about the top angel, do you know what it is in terms of x?
looking at the image I sent with the isoscele triangle
It should be the same as either the bottom left angle or the right angel. Which one of them and why?
well i thought the left and right angle were equal and the top is different than the other two -
it says that they are different the bottom left is 2x+11 degres and the bottom right is x-2 degrees
So the angels opposite of the two sides that have the same length are the angels who are equal
look at the image I sent to confirm that you see this
The pentagon to the right has an area of 7 square centimeters. If you enlarge the figure by a scale factor of 3, what is the new area?
is the answer 63?
I used a square. If the sides of the square is 2, the area is 4. If I triple the sides, the area is 36, which is 9 times. Then I tried it with a circle. If the radius is 2, the area is 4pi. If I triple the radius, the area is 36pi
so I did 9*7
Cool
So the way I see is in the new figure all lengths are increased by a factor of 3 like you just said
since area is length squared this factor 3 gets squared
so 7cm^2 in the first image becomes 7* (3cm)^2=7*9cm^2
Nice way of trying some shapes you knew ๐
thanks
How do I do proofs good
$prove:\frac{\left(sin\theta :+cos\theta :+1\right)}{sin\theta :+cos\theta :-1}-:\frac{\left(1+sin\theta :-cos\theta \right)}{1-sin\theta :+cos\theta :}=2\left(1+cosec\theta \right)$
A pOtaTo:
On the triangle ABC, AB=AC. โ BAC = 120ยฐ. Point D lies on BC and point E lies on AC. โ BAD = 80ยฐ and โ ABE = 20ยฐ
Find โ ADE
isnt angle ABC 30?
since 180 - 120 = 60, 60 * 1/2 = 30
i got all the angles but BED, ADE, DEC, CDE
this is what i got so far
you can do something with triangle ADC
to find angle ADC
should bring you closer to your answer
ADC is 110, BEC is 140
How do I perform rigid transformations on a triangle without a coordinate graph? These transformations are translations, rotations, and reflections. I know how they work, but I donโt know how to construct them. These transformations have to be conducted using a straightedge, compass, and protractor.
how would I start to do this?
image is blurry, are both those angles labelled as theta?
yes
angle bisector theorem
yes
I wrote this problem and solved it but if anyone likes, could you plz also solve it so I can see if I did the problem correctly? Thx
(also I put the problem in this channel since the problem's basically just a ton of applied trig)
what's the point of making it three blocks instead of two
aside from one of the parts
@upper karma send your work and people can review
is there a way to prove that the max value of a*sin(x)+b*cos(x) is sqrt(a^2+b^2) without using calculus?
yeah using the pythagorean formula or the R-formula or whatever else it's called nowadays
Hi, guys. I have a question. Given the volume of the pyramid is 500cm^3, solve for the height. Based on the formula V = 1/3bh, is this question even solvable or is the answer just h = 1500/b.
Hi guys! Can help me?
The following figure represents the flat pattern of a solid. The volume of this solid is:
a) 20 (Root of three)
b) 75
c) 50
d) 100
e) 100 (Root of Three)
Sorry if there is something wrong written by google
@upper karma base area times height! Also don't multi post.
Ok! Thank you!
@upper karma base area times height! Also don't multi post.
@novel berry
Thank you
First hint: what do the red lines represent?
Second hint: what is the sum of all interior angles of any triangle?
180
write it down as an equation = 180
I tried but I did something wrong
One angle is a right angle
x=11
Thanks
๐
Guys if you use the same reflection twice the object will land where it started right
0_0
What is 0 choose n??
Shouldn't it be n choose 0
Correct me if I am wrong it has 2 eight
2 right diagonal and horizontal
@olive portal
i donโt study geometry sry
Ah ok
can any kind ppl here help me out with this
Hey guys, can anyone help me with a Vector issue, its for a game engine. I want to somehow offset my vector v (indicated on the image), in a way that it's offset to the left and to the right. Kind of like raytracing in 3 directions to check for empty position to move to. But I have no idea how to approach this offset. I have T(x,y) (desired location), vector v and the position P(x,y).
I'd like to try and get something like this
are you trying to get it to shoot around that obstacle then?
do you know the width of the blocking thing or would you have to find that out
like I'm assuming you're like playing minigolf and you're at P trying to hit your ball into the hole at t, but there's a wall in the way, so you are wanting to shoot as close to the wall as possible to get around it
is that basically what you're trying to do?
Yeah
I can get the size of the obstacle
But the thing is, I can offset it to the side of the obstacle, but I have no idea how to prone and see how much should I add to avoid it
As depending on orientation it can be +-x, +-y
(these are units so I am implementing avoidance and going around
)
I'm not sure I fully understand but
what you can do is take the difference between a vector pointing to the corner of the obstacle and your position, that gets you a direction vector pointing exactly where you want to shoot
But wouldnt that land me exactly at the corner?
if your gun/ball you're shooting has width, add half the width to the vector at the corner
maybe add a little extra just in case that exact amount is absolutely too close
that make sense or should I doodle a little pic to show
Literally add? Doesnt it make a difference how the target is orriented?
yeah, of course
I don't know what that is
That's my biggest issue
well I can't help you with your problem if you don't know your problem
What?
I don't know what you're drawing
Oh
these are just triangles
P is the position we're at, O is the obstacle we're trying to avoid, v's are the vectors
We have a vector pointing at our target behind the obstacle(the middle one) and we have 2 vectors pointing exactly at the corners
Yep
blue vector is pointing to one corner, and orange dot is where you're shooting from
you need just enough offset to pass, ok cool
so our problem is now figuring out how to get that green vector and that solves the whole problem?
just want to make sure we're doing what we want here cause I'm not psychic haha
Yeah we're getting the green vector
ok what do we know about it?
We know the pink vector
the center of the obstacle
wait
We can use the center of the obstacle and the corner
I'd say we don't know the pink vector
I mean we don't know it because we don't know which side we're hitting
thats correct
we know the length of the green vector though, and we know the green vector and pink vector are perpendicular
well, let's not care about which side we're hitting
we can determine that beforehand
Alright
based on where p is relative to the left or right of the center of the obstacle
maybe we should do that first since it's easier
and logically happens first too
I am following
so here I've drawn a dark blue line where the projection will end up, which is to the left of the center of the obstacle
so it would really end up shooting to the left in our case
actually it should be computed as the center along the light blue vector, not the center of the obstacle, that doesn't matter
so you tell me, how do you compute something like this?
you're wanting to decide which side to shoot towards
and we determine which side to shoot to depending on whether p is to the left or right of the center
and we can look at that by checking the projection along the light blue vector relative to the center
you're shooting towards both sides simultaneously?
Sry @wise pawn this is a big complication, I'll try and research more on my own
And get some notes ready
It's a bother to ask anyone in discord this
I'll look at stackoverflow
well I'm complicating it because you're not paying me, I'm teaching you for free lol
I have the answer
I'm just not giving free answers that's all
Yeah that's understandable
I am gonna try this if you're interested in reading it https://gamedevelopment.tutsplus.com/tutorials/understanding-steering-behaviors-collision-avoidance--gamedev-7777
Where do I start?
Similiar shape
First, u want to add 60+100+120 together to get 280, then 360-280 to get an angle of 80 for F
yes
Then your gonna take the FECG and split it in half from F to C
ok
Now u should have two trinagles with the top one u have two known sides and and unknown side
yes
Nvm
Wait, missread, FECG is just like a shrunk version of ABCD, since the side lengths of BC is double EC, that means u can double the six the same way to get x = 12, 6*2
oh ok thanks
ABC is a triangle right angled at B.AB=5 and BC=10,what is angle C?
use your trigonometric functions
Yes?
degree or radians mode
Sorry I am new to trignometry
Maybe a bit bad as well
Could you please show me the solution for this?
,w
and this is a math server
Please submit a valid query! For example, ,ask differentiate x+y^2 with respect to x.
Use ,w
can someone help me solve arctan of 5/10
wtf is atand
in degreess
arctan in degress
its for Mathbot
but I forgot this server doesnt have it
i have never use ,w
Just do the same thing with ,w
,w atand(5/10)
If you want an approximation ofc
yes 26 degrees
Thank you
what's tand?
Oh
draw the height
$sinx=\frac{3}{\sqrt{10}}$
chene12:
Therefore opposite = 3 and hyp = $\sqrt{10}$
chene12:
note these arent exact side lengths, merely ratios
therefore adjacent = $\sqrt{ \sqrt{10}^2 - 3^2 }$
chene12:
adjacent = $1$
chene12:
image isnt clear enough
,rccw
i need some help, how would i write an equation to solve for z?
Consider the theorem of the sum of angles on a triangle
Alright
Where did you got to
If you got to anything
The key here is to notice how we can relate the angle 145ยฐ to the inside angle in order to apply the theorem mentioned above
Okay so yeah
We want to create an eqn to solve for z
And we can use
Consider the theorem of the sum of angles on a triangle
angle1 + angle2 + angle3 = 180 degrees
Yes
i'm still pretty confused, sorry
We want to apply that idea exactly the same way you'd do with numbers
Is the z what confuses you?
yeah pretty much
Okay how would you apply it with numbers
Imagine you have a triangle with 30 60 and 90 degrees
would z equal the 35 degrees?
,calc 180-45
Result:
135
i had a feeling
correct
So how can you relate those angles to 180 degrees?
do you mean 35 instead of 145?
@umbral cloud i believed it is not hard to understand that i'm helping and i don't like getting interrupted
so, 35 + 2z + (5z-2) = 180
Yes
okay, thank you
Yw
got it all figured out, thank you so much for your help bro @upper karma
Glad to hear!
I dont know how to do this but I think I've found AC/BC by using the sine rule? My result for AC/BC is sin(arctan(1/2))/sin(arctan(2/3)). Idk how to get AC/AB
Solve for angle C
whoops
The number of sides of a regular polygon is 18. Find the measures of an interior angle and an exterior angle for each ploygon.
i said interior 160 and ext 20
potentially
$180(n-2)/n$
The Sealman:
yay
how does it prove those two are parallel?
if they are the same
thanks for the help โค๏ธ
Well if the angles are equal then they are parallel
i mean the lines
it says 2 equals 4 proves p and q (transversal above) are parallel
any ideas?
converse of parallel line theorems
they didn't put that in the word bank, @silent plank
this is all i've got
Alternate int, Corresponding, Same Side interior, Alternate Exterior, linear pair, vertical
can you see that 2 and 4 are alternate int?
can someone help me find BDC , AB = AC
@upper karma what have you tried
a car with a mass of 1100 kg is travelling at 100km/h and collides with a tree and stops in 0.5 seconds. Calculate the force exerted by the car on the tree
someone do it adlays
Can you help me with this problem?
can you show what rules you have to choose from?
this looks like more of an issue with the answer format than with the underlying math
also @proven totem please please PLEASE do not post across multiple channels.
Sorry. My bad, just a newbie
yeah again i'd like to see the list of rules
there are a bunch of possible ways to do this, i just need to know what your system calls them
I don't think they will reply, I gave them the answer in #calculus which I shouldn't have done
what is B?
the answer to B is something you should know from theory
graphically, going between the graphs of f and of f^-1 is reflection along a line that makes 45 degree angles with both axes
can some1 help me out with this
think about the sum of the interior angles of the triangle, & how they relate to x, y and z
i do know the interior angles should add up to 180
180-(x y or z) = its respective interior angle
ahhh oh so u take out the 180*3 and then add 540 to each side
tysm that makes sense
hi
can someone explain to me why this is true
Why does AE = EG
and GF = FC
what property is this
oh can't believe i missed that
Year 9 coordinate geometry
lines with the equation 3x + ky = 11 and 5x + y = 8 are perpendicular, find the value of k.
so i have isolated the gradients and i know that -3/k * -5 = -1 (i think)
because they are perpendicular
Change from standard into y intercept form and find the value k for the slope in the 1st equation so thats is the negative reciprocal to the slope in the 2nd equation. m_1 => - 1/m_1
for example if the first slope was something like k/2 and the second was -1/4, then you know that k/2 = 4 so k = 8.
Can anyone explain how you determine if a fraction is greater than 2pi?
Wdym?
I thought the answer was just 1/6 and 5/6
But 13/6 and 17/6 were also answers
But 17pi/6 and 13pi/6 are both greater than 2pi
Do they give some sort of explanation on why that is so?
Oh I see
@teal mica the pi in the sin function is not part of theta's value
so it seems really confusing at first
Yeah it's independent from it
yeah, so as long as theta is greater than two pi, you can just keep on incrementing 2pi as it results in coterminal angles
as for calculating it, I guess you just gotta check if 2pi/theta > 1
Sorry kinda got lost there
no worries
I substituted pi(theta) with x
then solved for theta
Which got me theta = x/pi
Then solved for sin which I got 1/2
Then referenced it to the unit circle which got me the pi/6 and 5pi/6
right
Then I re-subbed my result with x and then solved
which got me to regular fractions
But i'm unsure how to determine if those fractions are > 2pi
Like pi/6 * 1/pi = 1/6, but how should I go about trying to determine if 1/6 is > 2pi
Yeah, I can't give you a truly simple way as pi is a tricky number to handle
but the best you can do is divide 2pi/theta
if its greater than 2pi, then the result would be less than 1
or no
you can just check if theta/2 < pi
If I divide 2pi/theta when theta is pi/6 that would get me 12, but not sure what that means too
theta would be 1/6
so theta/2 = 1/12 < pi
same applies for all other theta values
lets say i had something like theta = 17/2
theta/2 would equal 17/4, which is 4 with a remainder 1 or 4.25
Since thats greater than ~ 3.14
we know it doesnt satisfy the range
Sorry, my wording is sort of confusing
But there isn't really a clear cut way to figure out something like that without testing and checking
Hmm
If anyone would like to contribute please do^^^
Sorry, just trying to digest it
there are no fixed points in a translation right?
yes
thanks
pls help me
I didn't understand how this conclusion came up
the answer is P+ rQ where r is the required fraction right?
Looks complicated
Hi guys....can someone help me prove this identity please?
I've tried so many times but I get stuck and i can't prove it...help
Show your work
My work..? What do you mean?
What have you tried
Okay
So I changed tanร to sinร/cosร...then I expanded the brackets and then I added the fractions since they all had the same denominator....
After I saw there was a quadratic in sin so I factorised and then I changed cos^2 ร to 1 - sin^2 ร....then I'm stuck
,rccw
If you notice\
$\sinยฒ(\theta)-2\sin(\theta)+1=(1-\sin(\theta))ยฒ$
Use difference of squares in the denominator
The Godfather:
Use difference of squares in the denominator
Okay thank you so much....I'll go do that now
But guys....
It has to equal - sinร- 1 / sin ร + 1 ...like I sent in the picture of the question
But when I simplify...I'm getting 1 - sinร / 1 + sinร
(1-sin(x))ยฒ=(sin(x)-1)ยฒ
Show me just the last step
The Godfather:
Huh?
That up there was 1 - sinร = -(sinร- 1)
So what is sinร - 1 equal to?
The way they taught us to factorise instead of 1 - sinร....we would have (sinร - 1) (sinร - 1)
Which is what I have in the first pic of work that I sent.....
According to how I learnt.....this is how I'm supposed to write it and from here I need to work
Well you see
When you use difference of squares of you get
1-sinยฒ(โ )=(1-sin(โ ))(1+sin(โ ))
Now to cancel the term in the denominator you have to factor out -1
Factor out -1 from where exactly?
From any one of the term in the numerator
I got through
Lol I'm sorry to put you through that....
Thank you so much, I'm grateful
Yw
:)
I just need to know what w x and z are
Thats all I need help with
<@&286206848099549185>
Since the trapizods are similar, z is equal to 80, y = 105
I see
Then, since one trapizoid is scaled down from the other, u can take (25/10)*7.2=w
Then, its the same idea for x, except now u can make and solve an equation
(10/25)*15=x-2
Thank you for helping me out with this
Is anyone able to explain how to solve this by hand? I get how to solve via calculator... cos^-1(-0.123)... but what steps does the calculator perform to come to the solution?
Calculator uses Taylor series expansion
If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.
I am scare
Help
anyone know what this symbol means?
that is the greek letter theta, usually used as a variable for angles
thanks i thought it was beta cause i kept hearing my teacher say it
beta: $\beta$
ramonov:
@upper karma
Because you cannot cancel ANYTHING if there is any + or - in the fraction (that are not within brackets)
@night snow shit thanks so much
Does anyone know how I can do this?
@Mahjestic#9700 Since there are two parallel sides, (AB parallel CD, AD parallel BC), it is given that ABCD is a parallelogram. By the properties of a parallelogram, angle A = angle C
then itโs just simple from then on
Am I supposed to find out the values of s and t by substitution?
How do I show that $2(pta+qtb) โฅ0$? Or less than or equal to all the terms left side of it?
lazypawtato:
Can't promise to be helpful but I'll try.
For starters I don't know shit about parametric form of a line.
But nevertheless I guess you can translate an answer in regular form to parametric form?
yes
So consider that the two lines intersect in two points, (x1,y1) and (x2,y2). Then show that x1=x2 and y1=y2, and hence you prove that the point of intersection, if it exists, must be unique.
no I got that
Oh, alright. You're asking about that circle problem?
yes
Have you proven that any line passing through (p,q) must pass through the circle?
No that's what I'm trying to do
I tried to follow that hint
I understood that you can make points on line with distance to centre as the radius
I'm seriously oblivious of the parametric form of a line. I'll take a look at it quickly and see if I can add something valuable.
Okay thanks

Is anyone free to help me here
just post your question someone will answer eventually
@rain vigil use double angle identity for sin and cos
Hi guys. I have a question in spherical trigonometry. Given two points on earth A(\lambda_A, \phi_A) and B(\lambda_B, \phi_B), and 2 distances a, b. I have to determine all the points X(\lambda_X, \phi_X) on earth such that, the distance between A and X is b and the distance between X and B is a
Given two points on earth $A(\lambda_A, \phi_A)$ and $B(\lambda_B, \phi_B)$, and 2 distances a, b. I have to determine all the points $X(\lambda_X, \phi_X)$ on earth such that, the distance between A and X is b and the distance between X and B is a
moshill1:
thanks @humble pulsar
๐
@rain vigil use it to go from sin(theta) to sin(theta/2)
For sin(theta/2), sin(theta) is it's double angle
I have figured it out, needa use triangle form on first quadrant
Hello!
Idk if this is the right channel but it has the geometry in the name so yeah, my question is (this might be to easy for you guys but we just got started on geometry last week) how do i draw and label this
i just finished ch4 test and I am very confused on why one of my questions was wrong
my brain is hurting so low iq rn but
i said sas
because perpendicular form right angles
right angles are equal
pqr = psr
qr = sr is given, and pr = pr because reflexive
apparently the answer was not possible
i have no idea
help
helppls
ik some rules but like i dont think any of them deal with this
and i know like all of the angles have to equal up to 360
like x would be 7 right ๐
wait nvm i got it lmao
it was like 100 + 100 + 80 + 80 and x was 7
14 x 7 + 2
look at me doing stuff
anyone know how to do this
@indigo chasm mbos look up the equation for the volume of whatever trapezoidal prism that is
the volume of any prism is given by this formula:
$area = base_area * height$
$area = base_{area} * height$
chene12:
Volume =base_area* height?
Yeah
Find this angle using trig ratios
use angle a to find angle b (remember that they both add to 90 degrees)
Then simply use trig ratios to solve for z
there are other ways to do it too, see if you can find any alternate solutions!
@woven walrus
im not sure, i havent solved it 
well thanks anyways ๐
my pleasure
your 4th statement isn't given
what does: $\overline{BD}$ bisects $\angle ABC$ tell you?
ramonov:
Given?
no idea why you skipped line 1,
that's what's given, but what does it tell you about the angles involved?
geometry is my favorite
how
hello everybody i need help with bearings
i have no idea what is going on
9th grade
Have you sorted the possibility of posting the problem you are stuck with
@hushed spear
yes
well honestly
i have no questions
but i have this one
Alana hiked 10km in the direction N70E. Bree set out from the same point and hiked 24km in the direction 340T.
what is the difference between the two,
what is the true bearing of Alana from Bree,
and how far west of Alana is Bree, correct to the nearest km?
@upper karma
i have no questions
@hushed spear
I am new here, could you elaborate on what 340T is
it can easily be solved by resolving them into vectors if T represents a direction
My teacher said that the green line is tangent
Iโm not sure why
is it because when Sine=1 and cosine = 1
1/1 = tangent?
<@&286206848099549185> Is the slant height of a pyramid the same as the lateral edge height
Is this right
no
i need to fill in each empty box
ah i see
ok so i would do
1 is congruent it 7 (given)
6 is cong to 7 (vertical are cong)
1 is cong to 6 (transitive property????????)
measure of 1=measure of 6 (def of congruent angles)
measure of 1+measure of 2= 180 (linear pair)
measure of 6+measure of 2=180 (substitute m<6 for m<1)
yeah did u understand all the steps
yeah it can be confusing because there are a lot of ways to prove this
yeah
np
thanks man
Factor the expression and use the fundamental identities to simplify
<@&286206848099549185>
What's csc^3x and so on write them out
what should I do after I split up the exponents?
Show me your work
I thought about it and I just used foil
and then I can get (cot^2x)(1-sinx)
(I don't know if the way I got (1-sinx) is correct I did 1/sinx - sinx/sinx)
I've been on this for 2 hours I hope someone can help me ๐ฅ
Iโve been stuck on this question for a little while and I havenโt figured out the steps in doing it, If someone could dm me the steps in how to do it I would appreciate it (weโre only using sine/cosine law and sohcahtoa in this section of my math course)
There's a rectangle that's 4 vertices by 5 vertices and you need to find the amount of rectangles in it someone asked me that and I said 60 but apparently it's wrong
I don't get how it's not
If someone can help me with geometry and call and talk please dm me
Can someone tell me why is 20 being divided by 3?
The base is 30in and the height is 20in
is the term "parent function" referring to what the shape of the function will look like when graphed?
is anyone able to help me? ik its probs not that hard but im a bit confused bc im rushing this lesson
<@&286206848099549185>
their slopes should be equal in order for them to never intersect
find the pairs that make cd's slope equal to ab's slope @lament shell
wait so what numbers would i use, just random ones?
Test them
what pair of angles have to be equal for both triangles to be the same @stuck crypt
(Shouldn't be too hard as long as you know the AAS rule)
yea i figured it out i shouldโve read more carefully thank you!
Hi hi! So I'm struggling with hyperbolas (I'm only in high school dfhds don't judge me too hard lmao). I don't have a specific question, I'm just finding it hard to understand the concept in general?? If anyone is willing to help, I can send some examples of questions at the level I need to understand?
(I'm going to be on another tab, so if anyone gets to this can you ping me pretty please <3)
<@&286206848099549185> (I think I'm allowed to ping here? It's been 15 minutes. If I'm not supposed to, my bad bahaha)
@oak stag hey, I just came here for help too now, I'd suggest you to ask in other questions channel with greek letters beside it, because I'm doing that too now. Sorry for guiding you to an inactive channel
Ok, thanks โค๏ธ
<@&286206848099549185>
@bright hollow please, only call helpers after 15 mins of submitting your question and no one responding. And if this channel seems to be inactive, ask in one of the questions channel
@next jackal where should i ask then