#geometry-and-trigonometry
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@upper karma Your status fake information tbh.
Wait lemme get the video
Support my work on Patreon: https://www.patreon.com/melodysheep | Get the soundtrack: https://bit.ly/2HKl9fi | How's it all gonna end? This experience takes us on a journey to the end of time, trillions of years into the future, to discover what the fate of our planet an...
Wow you noticed my status
:D
That was at 1:32 and youāve been helping a lot of people since then and thereās been a lot of problems and it-
Yea, I would forget :(
Your status assumes that we are the only life form tho.
I specified humans
Oh wait
Life isn't humans tho.
No like life on earth
Bruhh.
It said that in the video too
Like the chances for you to be alive?
Like it was a ctrl c+ctrl v
No
The chances for you to be alive is like $\frac{1}{10^{2.5m}}$
leviosa:
How long life is compared to the whole universe time length
Until like all black holes die left and thereās nothing left in the universe
So time becomes irrelevant
"Life is possible for .0000000000000000000000000000000000000000000000001% of the universe's lifetime."
This suggests that the chance of life in general is that number in the universe's lifetime.
Yesyes, it was a line in the video
Itās not saying the āchance of lifeā
We haven't discovered even a fraction of the universe.
We only know that we're the only one.
Astrophysicists are using what they can to predict how long it will be until the āendā
What if, hypothetically, we are the only living things in the entire universe and there were no more planets of life to arise?
I also wouldnāt suggest we talk this out here
Wouldn't the chance of life in a universe's lifetime be 0.
And we'd be an outlier?
But thereās no hypotheses to this
This is near-accurate information from a factual video
From what astrophysicists know
I need help solving this
Alright, you can think what you want in the end ig, but Iām definitely not arguing here and I would agree with the scientific video. Keep talking if you want, Iāll just ignore you ig
That video is far from scientific.
Unless assumptions = science, then sure.
Umm what does that have to do with geometry?

why is that in here lmao?
Someone just attacked my status
ooooooh
wow
@upper karma Wow attack.
I only bothered to challenge it.
Well you were pretty aggressive..
And I thought you said youād leave?
Unless youāre actually helping..
Alright, you can think what you want in the end ig, but Iām definitely not arguing here and I would agree with the scientific video. Keep talking if you want, Iāll just ignore you ig
@upper karma As if this was not aggressive?
Lmao talking shit about me is helping.
Nice.
I think he just meant for a debate
Iām not? I literally just pointed out all the verified sources for you. Youāre saying all of those sites are wrong when itās the closest info we can get.
Not in this channel, oh no
In DMs, I would be fine
I only pointed out that your status was assuming that we're the only life form.
But I donāt wanna waste my time arguing
āYour status is wrongā
And then you went on a rampage on how your sources are superior to whatever anyone says.
All life on earth
Your status suggests life in general in the universe..?
Not my sources.. accurate, scientific sources confirmed by astrophysicists and other scientists
I literally just copied what the video said
Watch it before you start an argument
You realize one of their sources was "Google."
you might be misinterpreting @upper karma
Some google sites like .gov are accurate
Wow this is some pretty good geometry
Lol fr.
this is more than I learn in school
Then leviosa can leave and we can continue with actual Geo
Like they said they would
#discussion , or no?
I know, Iām trying
No itās fine lol
is number 2 even possible
@brisk ginkgo https://youtu.be/GppOSNTi5OA?t=717
This geometry video tutorial provides a basic introduction into circle theorems. It contains plenty of examples and practice problems.
Here is a list of topics:
- If a radius is perpendicular to a chord, it bisects the chord into two congruent segments. The point of conta...
Iām unsure on how to set up though @upper karma
@upper karma oh lol I see the video
Similar problem
Then measure angle STR is congruent to measure angle SUR because they share the same intercepted arc.
AO is 1/2 the diameter. The diameter is 8. So take 1/2 of 8 for AO.
Zezexx ^
@pastel anchor if the diameter (AC) = 8 ... the radius = ?
What is an inscribed angles theorem?
Wait wrong
Goosy ^
@upper karma 4
how to calculate the length of the arc?
how do you even find the arc?
You would multiply 32 by 2 PWE
why?
SUR is the inscribed angle
Arc SR is the intercepted arc
Yes, arc SR is 64 degrees
So how do you find the arc?
SR is the intercepted Arc of the inscribed angle STR
Ok thank u
@pastel anchor
Omg I gotta go out now
Np
Iāll be back lol
My mom be calling me
My brain broke
yea i said that already @upper karma
How do you find the length of a circle's arc
the entire thing is 360 degrees
and that quarter is 90 degrees
what do you think the measure of angle BCA is?
Goosy, youād use proportions:
i thoguht angle BCA was a typo
Wait the arc length can be in degrees?
Yes, thereās degrees for arc length and distance of an arc length
A whole circle is 360 degrees
^this is angle BCA
yea it just looks weird ig, most of the time at school they use the standard generic shapes
My eyes never saw this much math before
how would the formula look like?
send help pls guys last quesstion of my hw š
why did u divide by 56? i thought it subtraction
and isnt 7x suppose to be 7+x because it says "more"
why did u do 7x?
it probably should've been a vertical rectangle, right?
area of the rectangle is x * 7x
either way, it still the same thing
but wouldn't the "more" means its adding
oh, man...
I'm tired, and it shows
yes, you're right
it's really late here
I should be sleeping
np i think i understand now
anyone have a good trig book for independent study?
and since the width of the rectangle = side of square (which is x) ...
Try Israel Gelfand's Trigonometry @buoyant mirage
thanks
@buoyant mirage https://www.khanacademy.org/math/trigonometry
thanks :)
Wowww i didn't get a smiley face 
thinks OwO
all right, I'm off to bed
I posted the solution above
hopefully it's correct (I'm really tired)
g'night
can i use sin to find the angles opposite of 7
the angle to the left of the 90 degree angle
Yes you can
You can do
Arcsin7/sqrt74=Angle left of the right angle
$arcsin:\frac{7}{\sqrt{24}}=$ Angle left of the right angle
B):
And then just punch that into your calculator xP
Ah thank you!
$$\sin{(b - 1)\theta} - \sin{(a-1)\theta} = 0$$
$$\sin{(b - 1)\theta} = \sin{(a-1)\theta}$$
$$(b - 1)\theta = (a - 1)\theta$$
$$\theta ( b - a ) = 0 \Rightarrow \theta = 0$$
Daniel Cann:
Why is this wrong to solve for theta? Why can't you simply take inverse sine of both sides like this?
I did it correctly afterwards using a formula I looked up online for sin(A) - sin(B)
But I would like to know why this doesn't work
What function are you applying to both sides to go from line 2 to line 3?
Basically, "take sin off one factor" isn't a function that exists. @stark snow
^ generally arcsin(sin(x)) \neq x
also improper placement of parentheses
I was trying to do arcsin of both sides
$\sin(b-1)\theta$ implies $\sin(b-1)\times \theta$ which I'm almost certain isn't what you intended.
ramonov:
No
Well
It's what the book uses ahaha
But I agree, it's not really what I intend
But I mean sin((b-1)theta)
Ultimately yes, because arcsin isn't really a proper inverse to sin. It works only for "a part" of sin, and you have to reason your way out of the cases where it doesn't work
How does a right triangle with one of the angles being more than 90 degrees even work
in euclidean geometry it doesn't
Well someone showed it in a graph
can you show the graph
Said sin120 was 0.5 or something I'll need to check later
oh that
In this episode, I cover some of the more useful basics of trigonometry - sine, cosine, tangent, with more in depth coverage of sine. Ending with a coding experiment that renders a sine wave.
Support Coding Math: http://patreon.com/codingmath
Source Code: http://github.com/bi...
Around 5 min mari
Mark*
Like the opposite side literally flipped from the right side to the left side
Better have been sin(150degrees) is .5
Wait he said it was .866
the 120 degree angle is no longer inside the triangle
For sin120
Wouldn't it just be not a right triangle then why would the entire opposite side just appear on the left
Or is this one of those abstract things that I shouldn't think too hard on
@brisk ginkgo you need to find an open channel
@upper karma the 120 degree angle is not inside the triangle
There is A right triangle still, but it has a 60 degree angle inside instead of the 120 degree angle
The initial triangle has ābrokenā
Wouldn't it just be not a right triangle then why would the entire opposite side just appear on the left
it's still a right triangle
If you notice, itās not just the opposite side that had to move
So beyond 90 degrees the hypotenuse stops working?
In plane geometry, the sum of the INTERNAL angles of a triangle is 180degrees
And there MUST BE 3 angles
In a right triangle, one of the angles is 90 degrees
No angle in a triangle can have a negative measure
So both of the other angles INSIDE the triangle MUST BE smaller than 90 and sum to 90
It's still hard for me to grasp but I think I'm getting a bit of it
The right triangle that appears when someone uses an angle of 120 degrees is the same triangle as if they had used 60 degrees
It has just been turned around/reflected across the y-axis
I guess it's the whole turning around thing that confuses me. I keep trying to find a real example of that in my head but there's nothing
Perhaps it's just an abstract concept or something that doesn't necessarily have a direct connection to a real life phenomenon?
It is in a plane after all
Idk I just feel like I have a triangle and I extended it beyond 90 degrees, it'll just end up looking like those 2d pyramid shape triangles
But not necessarily equilateral, a badly shaped pyramid
In order to do that, you must abandon the right angle
What Iām saying is that you are correct, if an internal angle of the triangle is greater than 90 degrees there is an obtuse triangle that can be made.
@upper karma
@upper karma would it equal to 32?
I mean, look at where it's "opening" up to
it's opening up to a 64 degree arc
what do you think?
I thought it be 32 since itās congruent? @upper karma
it's an inscribed angle
same as angle SUR
did you not learn about inscribed angles?
didn't I link you a video yesterday?
Yeah u did
This geometry video tutorial provides a basic introduction into circle theorems. It contains plenty of examples and practice problems.
Here is a list of topics:
- If a radius is perpendicular to a chord, it bisects the chord into two congruent segments. The point of conta...
Thank u!
sure thing
all of them are congruent
(meaning they're the same)
because they open up to 64 degrees
and they're inscribed angles
so that means they're all 32 degrees
same as angle SUR, yes
they're all congruent to angle SUR
if they were to start from the center of the circle, it would've been a different story
(see the above video)
This geometry video tutorial provides a basic introduction into circle theorems. It contains plenty of examples and practice problems.
Here is a list of topics:
- If a radius is perpendicular to a chord, it bisects the chord into two congruent segments. The point of conta...
@brisk ginkgo
it's called "the chord-chord power theorem"
you really should watch that entire video
you might just learn something
if not, search youtube for "circle theorems"
pick a video
and always read the comments because sometimes they mess up
@upper karma thank u!
@upper karma can u give me a time lapse of which part to watch?
Oh ok
27:43
@upper karma thanks and neither of them is possible right?
do you really need to ask? ...
I mean...
if you multiplied them correctly, are you really not sure of the result?
5 * 12 = 6 * 10 ?
well?
are they equal?
4 * 9 = 6 * 8
again, equal?
also, why are you quitting Discord immediately
?
I don't... understand
Oh no Iām not quitting discord lol
is it because of the notification sounds?
it says you're offline
you need to have a little more confidence in your work
@upper karma literally exactly what my teachers say lmfao they say I overthink a lot
you have a calculator on your phone, right? use that to check your work
even though in general, you should avoid using one
because you won't have access to one during tests
or when you're in front of a whiteboard
We are allowed to use calculator in test
Ahah
Ok this one I donāt understand
UwU
@brisk ginkgo Very easy
For 2nd one, see if the intersecting secants theorem applies
And this for the 1st one @brisk ginkgo
Use google sometimes son
Google has many valid answers
Just interpret what is happening in the diagram
See how in the diagram it shows a tangent and secant intersecting
Like I didnāt use google lol
?
Thank u
Learn theorems son
I did use google but i couldnāt find it
Geometry is all about theorems
@brisk ginkgo Just interpret whatās happening inside the circle
You do know what a tangent and secant is right?
@upper karma wait PC? What would I do with 20 and 28?
Is 20 the length of the outer segment?
Look at the picture I sent u
Check this too, see how I just specified how a tangent and secant is intersecting.
Ok thanks!
Yeah
Alright š
Nope
I got 560=44
@upper karma for diagram B I have to do 4524 and 4923?
Why did my numbers change?
What
So both of them not possible
What theorem did you apply on the second one
Nm
Thank u!
š
Hello I need some trig help for class work
The equation is 4cscx + cot^2x=-5
š„ŗ
Ping helpers if u need to
Stop tagging 1000 different people for your problem
We know that:
$\sin^2(x)+\cos^2(x) = 1$
$1 + \frac{\cos^2(x)}{\sin^2(x)} = \frac{1}{\sin^2(x)}$
$1 + \cot^2(x) = \csc^2(x)$
Now, let $\cos^2(x) = \csc^2(x)-1$. Then:
$4\csc(x)+\csc^2(x)-1 = -5$
Didn't even waited the 15mins rule smh
Abhijeet Vats:
This is a quadratic in $\csc(x)$
Abhijeet Vats:
I hope you can do something with that
AMD:
solve for c
ok
@sullen pollen Still need?
yes
@sullen pollen The angle AKD is given.
Use that to get x. (180-that angle)
Then use laws of sines to get y.
Then use pythagorean theorem to get w (since you have 2 sides of that triangle.)
Angle AKD is 130.
x=130.
ohhh okay
i wouldn't say that 1 and 2 are no brainers necessarily
but my y and w were correct right?
my head is bursting š
so i would change the sin and tan from 65 degrees to 130 and then solve it again
?
x is not 130
130 is the supplement of x
because x is inside that little right triangle
@ripe dove so was my previous answer for x correct?
do you know how to solve for x?
yes, i know what x is
so x is 50
oddly enough, so did @upper karma earlier
Use that to get x. (180-that angle)
yes, x is 50
degrees
well, angle AKD and angle BKD are supplementary since AB is a straight line
and the sum of the measure of supplementary angles is 180 degrees
this should be correct? @ripe dove
@sullen pollen Ye.
Is anyone here good at identifying and proving trig identities? I am having trouble with them
Plenty of people, but you gotta post the actual question you want help with
Ah ah Iām sorry
Dw mate
Here is my first one
Okay what can you do on the spot.
You can do 2 things using trig identities.
Sneaky you help.
I gtg.
Bruh im in class now. Start by multiplying both sides by (1+tan^2(x)) since those fractions are ugly. Then notice that you have sin^2x+cos^2x which is equal to 1
See what you can do from there
Ok uh
?
No.
Don't listen to him.
@upper karma sin^2+cos^2=...?
Iām sorry I really donāt know
Oh.
I have the functions and stuff
Bruh you kinda need to know trig identities.
Huh what did i do wrong
@versed river Easier way to solve this.
All I know is this
A lot easier way.
Okay sin^2+cos^2=?
Oh wait Lima
*lmao
1
Alright.
Now the numerator is 1+cot^2
What is that?
Oh ok i see yeah thats mb
2nd collumn first row 
csc^2x
And then the denominator is 1+tan^2.
Which is?
3rd collumn first row 
sec^2x
Oh oh and then
Yeah the rest should be easy.
cot^2x/sec^2x is cot^2x
Yeah.
Wait no
It is.
Wait.
Wtf is that cot doing there.
csc^2/sec^2=cot^2
Yea thatās what I meant
csc^2=1/sin^2
sec^2=1/cos^2.
(1/sin^2)/(1/cos^2)=(cos^2)/(sin^2)=cot^2.
Basically multiply by reciprocal.
,w graph 4^x
,w graph exp(xln4)
is anyone good at geometry and able to help me?
could someone explain to me how it went from h/10 to 1/10 ?? (if u need more context i can provide - its an exercise on double angle formulae)
this step? both sides divided by h
aa right, ty
<@&268886789983436800>
@raw jay no offering money; against the rules
remove it from your msg
read #rules
is triangle ABC an isosceles triangle?
yes
Is it equilateral
sadly not
What have you covered so far in class
you need 3 things to solve a triangle, either one of these scenarios: AAS, ASS, AAA, SSS
Recipical Identities, Tangent Identities, Contangent Identity, Pythagorean Identities, Law of sines, Ambiguius case, Angle Difference Identities, Angle sum idnntities, etc..
cosine of what?
law of cosines
yes
it's missing the distance to the triangle
ok, how will you utilise that
Is AcC and BcC right angles
he said it's an isosceles triangle, so... if that's the height, then yes
True DSpider
they're right angles
I only caught on to what you ment about the congruent triangles now DSpider š
I forgot to tell u guys that this is a real life scenario question. The math teacher told us to create a clinometer to measure the angles. I just measured beta and it's 110
Hello Commander
angle beta is less than 90 degrees
beta is 25 hence
hello jc
with known alpha however now you actually know all the triangle's angles
UPDATE: this is wrong:
since 180-alpha should be equal to the two remaining angles of triangle which you obtain by extending height
and since one of them would be 90 deg you have half of an angle ACB
hence you have ACB as well
and is triangle isosceles? it is, so the remaining two angles of ABC are also known now
with three angles and at least one side you are done
and, actually, i suppose you implicilty have at least one side
UPDATE: this is wrong:
and you have one side also
so from this you can find the remaining two sides
and so on
wait...
155 + 25 = 180, it's wrong
you have two right triangles also
one with catet h and also catet 13+h
90-65 = 25 -> beta = 25
huh really
you have two angles now
because here is a mistake
it's not 25
alpha can not be just moved down if it still "points" to the C
i mean it changes the angle
oh yes, look i cannot draw it but if you move a down by 177 cm you ll be able to find beta = 90-65=25
so beta is 25 it is correct
ano
rough sketch
yes
it the only configuration that preserves alpha
um sorry to bother you guys, but I need help with math :/
that would also make the height of the triangle 177
@upper karma btw it is
@dire mural use another channel, this is occupied.
Sorry!
okay
bruh
is it a right angle
so we are actually able to find all the sides of rectangular triangle
and hence of original
my brain is exploding
i have a math test can anyone help?
@minor flower we don't help with tests
š¦
,rotate -90
here, all you need is to find AC and AB from sines/cosines theorem
what makes you think it's 25?
BC should be equal to 177
,rotate -90
here, all you need is to find AC and AB from sines/cosines theorem
@azure reef then you'll find AD from ADB triangle and by that you get DC and all sides
Does that makes any sense?
it does not give you anything since you are not able to find the sides
you have not enought data
follow my setting, it gives height and hence sides and two angles which is better
here, all you need is to find AC and AB from sines/cosines theorem
@azure reef where did u get 25 ° from?
alpha is 65
oops
š
a = 65
BC = 177
ACB angle is also right angle
to you have triangle ACB with three angles and side
from these you are able to find AB
and AC also then is derived
How is the angle 25? (the bottom left)
the issue then is to find BD or AD (-> CD)
How is the angle 25? (the bottom left)
@nocturne thorn because i just moved AB down by 177 units
so it is parallel
and preserves alpha angle
and hence presevers 90-a=90-65=25
^no
what?
oh ok
then you just use cosine and sine theorem and that's it you got all sides
oh that makes sense now
@azure reef thanks for your time
wait
how would i find the angles?
that makes a lot more sense now
thanks @upper karma
but, do u know how i can find angle CAB?
I got nothing
do they give you the area of the isosceles triangle?
because then we could get the base of the triangle from that (side AB)
Can i post graphs here?
yes
^
post the pic and a translation
Find S so that P is on the straight line a
the problem
i'm not good at geometry and first time we do it
and it's online school teacher just gives us homework with no explanation
translate the description?
P is the point (5,something)
i did translate
a is the line $ y = 2 x +1 $
What is the x-coordinate of P?
If you put that into the equation for a, what must the y coordinate be?
Malix:
I wonder if they will answer if every helper asks the same question...
uhhh idk
that's all the problem gives
the x coordinate of point P is 5
yes
now, can you graph that line?
what does y = 2x + 1 look like?
this is what it looks like
so s is 1?
yes i did
5;11
well, I mean they don't ask you for the size of the segment
just the y coordinate
how about now?
the horizontal line is the x axis
the vertical line is the y axis
so if you reach the x coordinate (which is 5) when you drag your finger on the red line...
you would also reach 11 on the y axis
yes
so P(5;11)?
and there's #linear-algebra for linear algebra related questions š
same thing
first draw the line
(make sure it's graphed correctly)
i just have to write it down
then drag your cursor/finger until you reach 21 on the y axis
good luck
but i have one more that i have never heard of
post it in #linear-algebra if it's similar to the one above
is it related to trigonometry?
it's something with Cartesian equation
if not, post in one of the free #help-5 [greek letter] channels
cartesian equations = linear algebra
no?
no
no š¦
linear algebra is about vectors and matrices and things like that
if you're just doing basic things with equations in 2 variables that's #prealg-and-algebra
no
huh
there's nothing to indicate the fact that the angle there is 30 degrees
there's nothing to indicate that this angle is 90 degrees
based on what?
On nothing :/
I found sides: x, y, h and angles delta and beta
how can i move forward
the problem is that triangle ABC is completely independent of the other ones
at most, they share the height as one of the sides
but
you can't use that information if you don't have the area of triangle ABC
So, it's a dead end?
to solve triangle ABC (or any triangle, really) you need 3 things
AAS, ASS, SSS, AAA
A - angle
S - side
you have neither
you only have the height of triangle ABC
which I suppose you could use half of the triangle (since it's an isosceles triangle)
but then you'd only have one side
yay?
oh, and I suppose you also have an angle
(90 degrees)
so you have a side, and an angle
you need another side or an angle to solve it
AAS, ASS, SSS, AAA
hmmmm, thanks a lot @upper karma
sure thing
like I said, if they had given you the area of triangle ABC, you could've extracted the base of the isosceles triangle, and had another side to work with
it was just notation
it's upside down
i mean it should be connected to the cosine and sine theorems
Ann:
this is a gamma
Commander Vimes:
where did yo get 30 and 60?
Unless there is supposed to be a variable somewhere
wait but if you changed it makes the whole thing easier
does it?
because 30-60-90 triangles have the shortest leg half of the hypothenuse
i mean sin30 and sin60 are table ones
but that still don't help you get sides a and/or b
and yes ^
i hate math now
btw, angle ACB should be quite small since it is anyway smaller than 30
I like how the building is irrelevant to the question but they decided to add it there
i firslty tried to understand what building is about
xD
yeah, post a pic of the problem
^
I'm in Algebra 2 w/ Trig, starting the IB next year
Oh youre just like me then, taking AA HL?
i'm taking AA HL next year
Good luck
xD
We'll be on the same playing field
wait but it does not look like there is an angle between your head and roof
wait wait looks like your picture was a bit wrong
Side AB appears to be the bottom edge of a quadrilateral not a triangle for one thing
^there's that
I just created a point C
and you're trying to establish the distances between you and those points? from a 2D image?
Consider all isosceles trapezoid in which we can inscribe a circle.
Restrictions are: sum of longer base and height of this trapezoid is equal to 2 (i.e. a+h = 2)
What are all values of a with those restrictions? That is, figure out all values of a.
Taken @ocean axle
@upper karma no, the assignment says how would they do it without leaving their house
They have access to 3D
You have no guarantee that the quadrilateral lends itself to an isosceles triangle
"Actual measurements are not necessary" - i think i'm allowed to assume that it's the case here
cuz it looks like an isosceles triangle
you can get the distances to those points, for sure
how much lateral movement do you have from your window?
1m wide?
1 meter
That looks nothing like an isosceles triangle to me
The other face of that roof, yes. But not that one
That one looks an awful lot like you could make it a right triangle with your imaginary point c though
lol now imagine how it was for ancient greeks who didnt have disc
Also, spitballing here, since you can assume line AB is horizontal is there a way to use the apparent difference of the angle from you to each of them to determine that length?
I can use a homemade clinometer, but I just randomly picked the angles that looked like they were correct
Well, you are supposed to ādescribe the processā not just get some answer
@nocturne thorn
this is how you get the distance to point A
same with point B
then you form a triangle
and you get the distance between them
no clinometer needed
just lateral movement
(at a 90 degree angle)
You are the absolute best @upper karma
this is similar to the ones from Khan Academy, btw
check your DM's please @upper karma