#geometry-and-trigonometry
1 messages Ā· Page 296 of 1
I have a question:
Let S be a triangle on a co-ordinate grid with vertices (x_1,y_1),(x_2,y_2),(x_3,y_3) , and Q=(x_q,y_q) be a point inside the triangle. Let R=(x_r,y_q) be a point on triangle S such that x_r is maximum, let P=(x_p,y_p) be a point anywhere on the triangle, and let "theta" be the angle PQR, and the length of the line segment PQ be "d", if the function f(x) is defined such that d=f(theta), then what is this function?
The way this question is phrased seems to suggest that there's an easy formula for the function, but I'm under the impression that might not be the case after drawing a sketch
it's okay
i worked on this for 6-7 hours now
i want to cry
https://www.desmos.com/calculator/bukr2zhy17
that is all i could do
i managed to work out point R
and the black bit at the top is the "d" value for the bit b/w P2 and the purple point
which is point R
that is correct
AA theorem is a valid answer
OMN=RPQ, and MON=PRQ
angles
so they are similar
2 pairs of corresponding angles will be equal
how much square feet do you need for a chicken
wat
so your animal is a chicken?
how many horses are you building your enclosure for?
1
okay, so you need an area of 4500 ft^2
20250000 ft
not really
no
it's not (4500 ft)^2 but 4500 (ft)^2
i did not say (4500 ft)^2 and even that AREA would not be equal to a DISTANCE of twenty million feet and change.
no what the fuck
418.1
yes
it's the radius of the earth
yes as in "yes i do not understand the difference"?
no yes i do understand the difference
anyway, #2 is asking you to sketch three rectangles which don't have the same dimensions but which each have an area of 4500 square feet
and to calculate the perimeter for each one
the dimensions can be anything you want so long as the area is right
so i just find stuff like x * y and y* z = 4500
no. three rectangles, not three lengths.
for example, you could have a 1 ft by 4500 ft enclosure.
oh
or a 150 ft by 30 ft enclosure
so i could do 2 * 2250
sure
how nice of you to label me a genius for essentially repeating what the problem states, almost verbatim
uhhhhhh can you screenshot lmao
if you really want me to make you check your own work
then what's the issue
is the area of this rectangle 4500 square feet?
yes
ok
for this one do i just find the perimeter and tell them the one with the least
o yeah i do
see how you managed to answer your own question with just a little bit of thinking about it
yay
is this good
4500 feet as its area
here we go again, with you seemingly still not understanding that FEET are for LENGTH while SQUARE FEET are for AREA
Someone check my question above qurax
i would help you but i dont know the midsegment formula
Ah ok
isnt the midsegment the average between b and c | a
x looks fine
what about your calculations for z
okay so since when did we require that the dimensions of our enclosure be whole numbers
i thought that it wasnt allowed
you thought that what wasn't allowed?
not having whole numbers
why?
a square with sides 67.1 ft long will enclose the necessary area (even going a couple of square feet over) but have a perimeter of 268.4 feet, which is less than your 270.
whats the formula to find it then
ah here we go again, the "what's the formula" mindset
honestly ive had enough of this lol
o
Develop some intuition, figure out the formula on your own.
Doesnāt help you to learn how to eat if the other person is holding the fork.
Hence, your parents stop feeding you at a certain age.
So get some muscle
ok i will find the formula
ok
If you need help, just post the question and Iāll help you derive said formula.
p = 2x+2(4500/x)
Is that a question?
and to find the smallest perimeter using the area
square feet*
and the square feet is 4500
Because if not then the smallest perimeter given the area is a circle
youtube
ok
So the question is like: āfind the smallest perimeter given x areaā?
And it has to be a rectangle
yeah
Ok well...
If the perimeter you gave is in fact the smallest for the given area, how do you know itās correct?
Like how can you trust the formula? Did they explain it?
i watched that video
and i watched another one
and both of them use the same formula
Ok, did they explain how it worked?
no
Thatās sad
Whatās the formula?
I need to know how it works before I am ok using it
p = 2x+2y then i did y=4500/x then i removed that x then i did p=2x+2(4500x/)
then i did p=2x+900/x
then i did p=-900/x^2
9000*
then i did x^2=4500
yes
And given one side itās a series of algebraic manipulations to find the other... not too hard then
Do you have a picture of the shape?
Or the question
Iām going to do it and then we compare answers
ok
It gave you the answers, you want to know how it got to them?
no those are the wrong answers
i think its 67.08
for the size
can u tell me ur answer then we will compare
theyāre the wrong answers
?
yea
i put them myself
but they are wrong because i did not acknowledge decimals
so im asking if you could solve it
and then we will compare
uhH decimals
perhaps
What are your dimensions?
For the rectangle after you gave decimals
4500 square feet
and the smallest was 750 * 6
of my examples
but i need to make the smallest
donāt think so
bc i just submitted it lol
Well idk m8
but i think its right
I do too
:D
sorry
Today I am a dingus
Square root ensures all sides same length... long as they donāt give you a side length itās good
š
I'm having trouble with this problem:
A right pyramid SABCD (AB = 12) has an inscribed sphere in it with O as its center, and has an altitude of SH. M is the midpoint of AB. The pyramid OHMA has a circumscribed sphere around it, and its radius is equal to the previously mentioned one. Find SA
I feel like I'm so close to figuring it out but I just can't
I can send the geogebra thingy I made for easier presentation: https://www.geogebra.org/3d/evxdqqrj
(I chose an h that would be close enough to what I did with sliders, I didn't actually find it)
I figured out that the OAH angle should be 30° and found the radius
I also have an equation: h^2 = x^2 - 72 (h being the altitude, and x is SA)
I feel like I need to find the ratio of h and x using the angles or something, but I just can't seem to find how
@upper karma what occupation would knowing quadrilaterals be important
In general knowing them will benefit you I guess
what have you tried?
@finite vigil don't ghost ^ 
this is not chegg you lazy cow
?
That's not an honest thing at all
It will affect yourself negatively, mind your actions.
someone was just giving me answers
Damn
I'm partly glad thay you decided to try understand instead of blusting it and pass the homework with a hole of knowledge
$s=r\cdot \theta$ where $\theta$ is on radians
@finite vigil
Alšdium:
Pretty much it
I have no idea
On what?
@finite vigil you have the radius, you have $\theta$ on angles, all you have to do is put it in radians
Alšdium:
And plug it into the formula above
To put into radians basically, you should blatantly know what 90° is on radians, if not, $90° \cdot \frac{Ļ}{180°}=$your desired $\theta$ on radians
Alšdium:
You don't know what? All good now? @finite vigil
@finite vigil copy and paste the question
ok
Don't do it wtf
Are you really gonna post your pictures with no context again and i still don't know what you did on the one before?
no
...
so its asking for
Are you really gonna post your pictures with no context again and i still don't know what you did on the one before?
.
......
I'm sorry..
i don't think they have the correct attitude to accept any help other than be guided through completely
@eternal crag so that means you cant help
like how yall gon start helping
and if she doesnt understand
you just give up
what part would attitude be put into that
are you stupid or don't know how to read? al3dium gave a formula, she replied "I don't know", al3dium then ask for clarification on what she doesn't understand, to which she then replied: "idk i'm fucking stupif" and "kms"
what the fuck are we suppose to do?
you tell me
should al3dium try to clear any confusion without knowing what the confusion is?
should al3dium just give the answer?
that doesn't mean i can't help, that means i'm unwilling to, i think the other party is not trying hard enough because she refuse to tell us what she doesn't understand
someone should ask
al3dium did, and he is not going to do it again
i don't know what to tell you
are we suppose to chase people to work hard?
nobody has the time to do so, helpers don't get paid here
either they're going to do some think on their own and show some efforts, or there is no point to continue
i feel like if you do not wish to help, that's perfectly fine! however, i would say that insulting people and vehemently arguing against helping might be more the opposite of helpful and could prove detrimental to the atmosphere, especially if someone else is happy to try and reach out/be understanding
yeah i got mad respect for yall i think it's a really cool thing that you're doing (and people can def be hard to interact with sometimes)
oof that sucks
also i missed a comment and would like to add that if anyone feels bad they could consider helping instead of expecting others to do it for them?
uh that was not at you at all, that was in response to the person who kind of started the end of the above conversation which made me realize i wasn't exactly very fair in my first message. now i admit i probably shouldn't have said anything in the first place. so i apologize for making this more messy than it already was
How would I solve this problem?
@gloomy slate
Ok
Yes just search up a bunch of theorems
And watch YouTube videos
Or use google
Pretty easy
@gloomy slate
oh nice thanks man
lol
hey
if nobody is in the middle of a question
Id like to ask one
Im not quite sure how I calculate the perimeter of this shape
How do you simplify,
tan(2t+pi) ?
Alšdium:
@mossy plinth yes.
Oh, thanks.
Np.
@mossy plinth if you want, you could use double angle tangent
what happens if i rotate a shape 180 degrees?
if you rotate a shape 180 degrees then itās rotated 180 degrees
not much to say
In this question, it is asking which lines are parallel
but im confused why isnt the 68 equal to 64?
I feel it might be a textbook mistake
cause answers are
DE ll GF ( alternate angles are equal)
DG ll EF ( alternate angles are equal)
:/
only DE || GF
Maybe textbook has mistake
<DGE and <FEG are alternate angles but aren't equal thus DG and EF aren't parallel to each other
hey um
I'm kinda having trouble with this equation
I feel like I know how to start but I have no idea what to do next š¤
let sin(x) = a, cos(x) = b
you might see something familiar
if you don't, ping me
@cinder portal yeah that's the thing, I did something similar to this and got a simpler(?) equation, but I don't really see what to do next š¤
now I have this:
2a/b = b^2 * (1 - (a/b)^2) * (9(a/b)^2 + 4 * (a/b) - 3)
What is this
can anyone help me with some geometry questions??
What have you tried
i dont know how to get the measure of triangles
i still dont get it
Properties of angles and parallels?
no how to get bdc by parallel lines
do you know how to identify stuff like:
alternate angles, (interior/exterior variants)
corresponding angles
vertical angles
no how to get bdc by parallel lines
Opposite sides of a parallelogram are always parallel
yes
How are <ABD and <BDC called?
Yes
ok thank god
Any properties of alternate angles?
do some angle chasing, see what you can determine
What does isosceles trapezoid mean?
Do you even need our help
which g?
g=125
but its 55 and 7
70
what about this one
i dont understand it with the diagonals and variables
Yes
its 12.25
,w 7x-6=3x+43
a2+b2?
it says solve for x
rounded to one decimal place
i know the diagonals are 12.3
Aight then we done
That's useless
The problem asks for x
that's the size of AB
it doesn't ask you to solve AB
its 12.25
the answer
the "diagonals" aren't ~12.3
you equated the two diagonals and solved for x to get a rounded value of 12.3
what do you know about the diagonals of a rhombus?
Are you even thinking about those problems or you are immediately posting them?
...
don't round until the end
im immediately posting them then im solving them
@arctic vortex
don't do that
use your head
rounding prematurely will lead to inaccurate answers
using 16.76 is still rounding
what how
round at the end
you shouldn't
rounding at the end?
yes
specifically the length of a side is sqrt(281)
and you should enter 4*sqrt(281) into your calculator for the perimeter
yes
thats the answer correct
i dont understand this one bc its like the variable one
how long have you thought on this problem?
3 minutes
ok
4.4 repeating is X
@silent plank i dont know
because its repeating
it could equal 35 or 36
x
use fractions and/or don't round until the end
ok
40/9
8 * 40/9
35.5 repeating
320/9
y = 64.4
repeating
@silent plank
and round that to 1dp
wdym?
8x + y = 100
y = 100 - 8x
yes
on what
DE = 72 thus EB = 72
Then u know what to do
DE = 72 thus EB = 72
easy to "prove"
ok
yes
did u get the answer
im solving it rn
im sorry, but what the hell is this
am i just being stupid
how am i meant to work out PQ?!!!!
@placid night similar triangles
haha i was first
xD
Seems awesome
Question asks to find ratio of TAN Z. Is it better if I leave it like that or should I further simplify to 3/4
Uhh idk, but I think both are fine
Ok
This look good?
Ok thanks
triangle definition of trigonometric functions got me slow
unit circle was easiest one to remember
but I don't think you should learn unit circle just yet though, since you're just starting out on trig
Yeah thatās why Iām practicing rn ahead of time I struggle with this part
Howās this
Ah ok
what was your answer?
27.4
I just used h to represent missing side
usually in the context of right triangles, h would be used to represent the hypotenuse
using it to represent something else can only cause confusion
although the question isn't phrased the best way, it seems they want you to find the side indicated by the variable x
I think I see where I went wrong Iāll re do and @ when done
I tried Iām not sure all I know is you use cos
only just saw you stuffed your diagram too
relative to the 19° angle,
would x be adjacent or opposite to it?
Adjacent
is x touching the 19° angle at all?
Itās not
then it would be the opposite side right?
Yeah
and then apply the proper trig function to find x
Ok
no
To explain this I need help I know it canāt be sin as im given the adjacent side
so you have an angle, the side adjacent to it, and you want to find the hypotenuse
which trig function relates those 3 things?
Cos

standard process:
location of the two sides relative to the angle you want to use.
which function relates those 3 things
@silent plank your a beast with math man you are goals
as mentioned before:
although the question isn't phrased the best way, it seems they want you to find the side indicated by the variable x
NOT the blank unlabelled side
Gotchu
That is vague, but yeah it has to do with that
Yeah hold up
Btw the angle at the center has the same measure as its corresponding measure of the arc
Look
Click on it
Now that part is set up.
The visualising part, we will look at this theorem, do you agree that $\angle{CDE}=\frac12 m\angle{CAE}$
Alšdium:
@tropic tide
O I see
Now
Notice that CAE=CB+BAE
@tropic tide will you not answer if i don't tag or what?
Can you be more participative at least...
š»
@meager rapids yes
show work
why are you using cos?
HELP anyone ??
you've even labelled opp and adj appropriately on the diagram
which trig function relates the angle, the opposite side and the adjacent side?
can i ask ??
find an open channel
Tan
yes
I got 16.1
x should be less than 14
rounded to 1dp, yes
Aight thanks
hello, is someone ready to help right now?
@rich mist hope this helps
i see youre supposed to keep it in terms of pi, when you do cos^-1, keep it in exact form then do 2pi- x to get your principle pair
can someone check my math
I have to simplify the expression: 2(2sin(x)cos(x)) (2cos^2(x)-1)
So first I expanded the 2 into 2Sin(X)Cos(X) and got
8Sin(x)Cos(x)*2Cos^2x-1
From there I used distributive property and got
16Sin(X)Cos^3(X)-8sin(X)Cos(X)
But then apparently the answer is 8sin(x)cos^3(x)-4sin(x)cos(x) (I've used x as the variable for theta). Idk what I did wrong?
8*2=16
like I expanded (8Sin(x)Cos(x)) (2Cos^2 x-1)
So first I got
16Sin(x)Cos^3x
and then expanded into the -1
And got -8Sin(x)Cos(x)
so combining I got
i don't get it
how'd you get the first expression
8 sin(x)
how'd you get the 8 in there
yes
I expanded the two into sin and cos
what does that even mean
so I got
4sin(x)2cos(x)
I did foil
$2(2 \sin(x) \cos(x))$
polynomial:
polynomial:
why is it not
what
4sin(x)2cos(x)
$2(5\cdot10) = 2\cdot5\cdot10 = 5\cdot2\cdot10$
polynomial:
polynomial:
polynomial:
$a(bc) = abc$
polynomial:
not really? it's just a "math thing"
ok I think thatās where everything went down hill
@digital perch which one?
First part
cos(27)?
Ig you aren't allowed to do it with a calc, and you have to do it with trigonometry, right?
Bc the instructions are unclear from what you cut off
Yeah
am i correct here?
No ...
No it a summer school homework
mhm
Are you familiar with the unit circle?
Uhh how are you expected to do this? Bc i may not want me to drive you to a new method you don't know
I just wanna know the basics to solving those questions and I will check in with my teacher for further clarification tomorrow
Ok
Ig i should introduce you the unit circle
Extending SOH CAH TOA so that we can define trig functions for a broader class of angles
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/e/unit_circle?utm_source=YT&utm_medium=De...
K am ready
Cool
The coordinates works like this (cos(x)), sin(x))
So you said you wanted the value of sin(60)
Look at the unit circle and find where it says "60°"
Now to find the value of sin(60) after you found the 60°, just look at the coordinate
No, Ļ/3 is 60° on radians
We are looking at the coordinates
The coordinates works like this (cos(x)), sin(x))
@upper karma so you should look at the second one as you are looking for the sine not cosine
(1/2,square root 3/2)
yep
The coordinates works like this (cos(x)), sin(x))
@upper karma so which one should we take? ^
1/2 or $\frac{\sqrt{3}}{2}$
sin(x)
Alšdium:
square root 3/2
Alšdium:
And you should leave it like that
but the question said to solve to the nearest hundredth
You didn't tell me that ...
Lol
,calc (sqrt(3))/2
Result:
0.86602540378444
@digital perch ^
yea
The case on cos(27) is to get an approximation as it is what is asked, by typing it into the calculator
,calc cos(27)
Result:
-0.29213880873384
Approximate correctly and you are done
ok thanks for you help (man/lady) idk but thanks
have a great day bye
I did x=cos ^-1 (4/5)
Correct but its not x, its theta. @meager rapids
šš¼
degrees to 1dp, yes.
I did 12/sin18
@meager rapids your correct
Is that good?
hyp is wrong
Hyp is 18
I meant like triangle would be similar by a shortcut
yes. they will be similar
šš¼
the use of "the same" implies congruency, not similarity
so use the proper terminology
The error would be that he would need to multiply 1.5 to both 8.25 and 18 and then divide them?
This person only multiplied it to 8.25 and not 18
Right?
no
the error would be with how they setup the ratio
the algebraic manipulation being performed was actually fine
they should be starting with
$\frac{\text{length}}{\text{height}} = \frac{18}{8.25} = \frac{x}{1.5}$
ramonov:
Ok I gotchu
cross multiplication is excessive
you only need to multiply both sides by 1.5
no
$\frac ab \times c \not\equiv \frac ab \times \frac cc$
ramonov:
I did, I multiplied both sides by 1.5
no
you didn't
you multiplied one side by 1
which was what i was trying to point out
Oh wait I think I understand now
NO
well i mean technically that is mathematically valid though
but doesn't help you
$\frac{18}{8.25} \times 1.5 = \frac{x}{1.5} \times 1.5 $
ramonov:
Oh thatās much cleaner
$\frac{18 \times 1.5 }{8.25} = \frac{x \times 1.5}{1.5}$
ramonov:
$\frac{18}{8.25} \times 1.5 \neq \frac{18}{8.25} \times \frac{1.5}{1.5}$
ramonov:
So the answer was right before (2.2) I was just setting it up wrong
no
did you understand how to get to:
$\frac{18 \times 1.5 }{8.25} = \frac{x \times 1.5}{1.5}$
ramonov:
should probably use exact values unless specified
Usually itās rounded just doing some practice to get used to it
then its fine
what's the question here
find the area of the grey region?
is there any more information given?
such as, do we know the big hexagon to be regular?
i think it's probably hexagon is regular and semicircles
@upper karma do you know how to find the area of a hexagon
what is it
as opposed to irregular semicircles?
..so what's the area
uh
i am pretty sure that's not the area of it
yeah
yeah..
wait
so you already solved it
what's the problem then
lol
what does that even mean
"trig" is the study of triangles
you just said you broke it up into triangles
so you solved it using trig
lol
yeah no thanks, have fun tho
,w define trigonometry
this actually fits
since equilateral triangles imply something about the angles
š
A brief description and guide on how to use me was sent to your DMs! Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
aight so do y'all wanna clown around or do y'all wanna actually solve this problem
but he said he already solved it
@upper karma the area of a circular sector with radius $r$ and angle $\theta$ is $\frac12 \theta r^2$ (where $\theta$ of course is measured in radians)
Ann:
you can do some trigonometry to write down the area of an equilateral triangle as $\frac12 a^2 \sin(\pi/3)$ where $a$ is the side length
Ann:
How to find alpha
I know alpha is 50.
But i checked answers, and it says
alpha = 50 (co-interior angle, FI ll GH)
but its not co-interior..
cause 120 + 50 = 170
not 180?
help?
gamma is 10?
120+50+gamma=180
Yeah but isnt co-interior
just 2 angles?
cause co-interior angles on paralell are adding to 180.
or do both
:/
if your book used cointerior angles
?
you know red and blue add to 180
oh
so alpha+64+66=180
Oh!!
you got it now?
nw
Is it 240?
Yep.

I believe Iāve gotten (x+3)^2+(y-6)^2=5
something looks off
specifically how did you get 5?
I have to rewrite my work for it to be legible lol
yes do that
now that's much better
Thanks guys
No clue how to do this
Right triangle?
They didnāt specify
Got it
Show