#geometry-and-trigonometry
1 messages ยท Page 165 of 1
I suck at my classes :(
Does anyone knows a chemistry server? Sorry to use this channle but general seems busy rn
Chemical science is chemistry?
I think so
In a parallelogram, prove that the sum of the squares of the diagonals is equal to the sum of the squares of the sides.
In this I was able to prove it, if the parallelogram was a rhombus
But I can't do it with it being a parallogram
ive tried many methods
but i can't seem to get it
i think i have to subsitute somehow
find one in terms of the other using one equation
then substitute in the other equation
it always becomes and uneven number
it doesn't
go on
i don't know where to go from there
when i try to go futher it goes to, 425(-2y)-y=40
oh yea
k
yay
i got y=11
thank you so much i completely forgot that's how you are supposed to do it
๐
Assuming this a kite
If mโ GHJ = 90 and mโ GKJ = 110, find mโ HGK.
<@&286206848099549185>
80
@cyan sonnet how
I have one more related to that kite if you could assist with that as well cause i'm... dumb!
If RJ = 3 and RK = 10, find JK.
Answer is the square root of which number?
is it
100+9
sqrt 109?
cause pythagorean idk to spell
yeah, sqrt 109
explain first one?
well, it's a quadrilateral so mGHJ, mGKJ, mHGK, and mHJK add up to 360 degrees
pretty much
@cyan sonnet since you're here
you can also see that GHJ forms an isoceles triangle
I'm not anywhere where I could graph and answer that right now
but you can graph it (or just imagine it in your head if you can), and calculate the lengths of the sides
which will help you with that
ty
np
so yeah, you can just use the distance formula to calculate the side lengths sqrt((x_0 - x_1)^2 + (y_0 - y_1)^2)
kk
if you're still available.. I just need help with one more. I am grasping this topic, but the teacher didn't really teach us it.
sorry for making u do my homework
@upper karma i'm dumb pls help l ma o
what numbers do i use for pythagorean theoem
it's not a right triangle
oh
nvm
it is
LOL
same
ok ill solve it if you want?
i mean
i knwo the theorem
just not what to put into it
my teacher isn't the best
you know how thatis
i just wanted to know because i dont wanna apply something you never seen
yea
nothing else
So RK which is the opposite side is = 5 and RY which is the hypotneus is 13
@sudden stream
Back
so let us replace
ok
yea
144
nice
lel
how old r u btw
if you feel comfortable answering
@upper karma SO answer is 144?
o
ty
i wish i had a better teacher tbh
she gives us assignments sometimes
of stuff she didn't teach
so basically the triangle of KY is 12 do 12x2 because you got half of the triangle and that is the value of the triangle which is 24
anytime
i have one more but i'm not gonna ask it cause i dont wanna seem more supid l0l
unless u wanna help
@upper karma u fine with helping?
on one last?
Lol ok
k
ill help
Dang you were fast
ty haha xD
you will make a fine mathimatician
lmao
stay in school kid
i love school
good job
NP
Can somebody here online help me with this question? I got it right because of my friend, but I wanna know how to solve it.
Quadrilateral ABCD is a rhombus. Point E is the place where the diagonals bisect each other.
If mโ CDB = 6y and mโ ACB = 2y + 10, find y.
<@&286206848099549185>
draw it
tag the angles
?
cdb is 6y
yes
ok
same for acb and the similar angles
Ok like this,
See the little "6y's"
o i did it wrong
woops one sec
This right? @neon fossil
how
i dunno
you only have angles
oh, well
my teacher didn't teach this AT all
2y+10ยฐ + 6y = 90ยฐ
Hmm
Straight lines AD and BE pass through point P of median CF in triangle ABC, where D and E lie on BC and AC respectively. Prove that AB is parallel to DE.
i can use ceva's theorem to get that BD*CE=DC*AE but that doesnt seem to help
and i cant find any similar triangles either
<@&286206848099549185>
@sudden stream Ankatic To use the pythagorean theorem you need to have the numbers outside the triangle
only apply for these types of triangles
and if the questions is to calculate outside the triangles then all angles equal to 180 you alredy have the answer which is that little square on that triangle that = 90 degrees
๐
What is the equation defining a torus?
Hi?
Or somfin like dat
Sorry I cant print screen. The test locks down my computer
I'm completely lost here
I know b ~= b is the reflexive property
But then which AA similarity are they talking about?
did you just say "sorry this is the only way I can cheat, please help"?
I'm not trying to cheat.
isn't this a test
I already submitted my answer
I'm just pretty sure it's wrong
I just need help with an example question
so you want to... cheat?
No. I can't resubmit it
My teacher only looks at the first test
you want to prove pythagorean theorem?
Yes
I know how to proove it on my own
but I have to complete their proofs
@sick socket is that timed?
No
it's a test tho right
Thankfully it's teacher graded as opposed to computer graded
so do you want me to prove #3?
My answer was the division property
ok i proved it
:/
its like 1 from thousands
q*q
now how can i send
:/
proof for #3
There's no numbers here
let me help in this one pls
Also like I said, I can't resubmit it for any credit. So it's not cheating. I just want to know what I did wrong if anything.
how can i sendd
q-q
ok ill do it in your triangle
rixor send your triangle again pls
omg and my notes are so good
:9
ok
so you see two triangles
and you see that there they have 2 right angles
Yes
so we make property:
Property?
ye
cause it is a similar triangle also: note: x + y is same as C
for triangle 1) x is same as a
and a is the hypotenuse for triangle 1
so property matches
now by that property
But what is property in this context?
similarity ๐
I have not heard that word at all in this course
2 similar side division
Oh
and that is:
so we have 3 informations:
now we do this:
So a/x = c/a by the Hypotenuse Leg Theorum?
Not how to get from point A to point B but what each step in doing so is called
one has x for right leg; a for hypotenuse and h for base
you use triangle similarity:(
ok ill post latex by steps
It's a/x = a/c not that
According to the test anyway
ye
same
that is just hypotenuse devided by right leg
๐
its just my thing turned around
hi
no idea
< has no idea what he is doing
you're being asked, in both cases, to approximate functions of the form arcsin(a)
which method have you seen to do that?
Wait i just put it in the calc right
if you have a calculator, sure
Anyone understand functional values?
what's that
(-5,8) f(x)-2
????
do you have a picture of the question you're trying to do?
or any more information to do with it
He did in #prealg-and-algebra
Tex the farmer tethers a cow by a piece of rope 50 meters long. The rope is fastened to a hook on a barn that is 10 meters from the corner of the longest side( and on the longest side ) of a barn measuring 60 meters by 30 meters. Over how much ground can the cow graze?
I need help with this problem
Tex
have u tried drawing a picture
idk how to draw the pic lol
ok
np
ah
is the area that I need to find the one inside that rectangle
like that part of the circle
not quite
i have mistranslated it and thought the cow was hanging on the rope on a barn thats 60m high and she is now hovering above the ground
hmm
lol
from what it looks like, graze means eat fresh grass
(and not levitate what i thought it means before, for some reason)
if the barn wasn't there, the cow would have the whole circle to graze on
oh
but the barn is in the way
@copper valve chalkboard! Such ancient technology >_>
chalkboard is the past and the future
and the present by intermediate value theorem
xD
aye so you just take the content of the circle minus the area taken by the barn that is a rectangle
within the circle only ofc
the cow is attached to some sort of rope
yeah
and assuming the barn has walls
can't just go through the barn to the other side
has to go around the walls
so really we'll have a shape sort of like...
lemme draw it
owo
eh pretty much gives the idea
nope
๐ | deadontheinside has given @upper karma a reputation point!
oh yeah its not that area
oh its a rope 50m
so it is that area
reposting question
dex the farmer tethers a cow by a piece of rope 50 meters long. The rope is fastened to a hook on a barn that is 10 meters from the corner of the longest side( and on the longest side ) of a barn measuring 60 meters by 30 meters. Over how much ground can the cow graze?
wait what
are you sure that part there aint involved @copper valve ?
i mean practically not but
ya cause the rope's not long enough
its not supposed to be that hard of a math problem
no ?
unless skarz' teacher is pretty hardcore
wouldnt want that teacher i tell ya
well it's gonna use some Pythagorean theorem
he's hardcore
okay so that part is involved
I have 4 problems like this to do
and it's due tommorow
:/
i know ya feel
also got stuff due tommorow
basically since you can't go through the barn, u have to go around the walls
isnt it um sum of lots of quadrants
hm
hulk cow can crush through the walls
draw it some muscles and the second part of the math problem is gone
.
sorry dude german humor, would work on the teachers here
but there is no grass inside the barn yo
hยฒ=10ยฒ+30ยฒ=1000
h=10โ10
then the radius of the arc at the top will be 50-h = 50-10โ10
since the barn is rectangular, those two angles will be equal
so the arc angle will be arctan(30/10)
yee i knew it, that part wont be necessary
@runic jackal it's not quadrants cause the top arc won't be 90ยฐ angle
since the cow is posted 10m from the barn
not directlyโ on the corner of the barn
hmmm
oh
no we still need the angle tho
@tropic stirrup is there a way to do this cow problem without trig
๐ค
there might be a way to do this slightly simpler but it should still involve some trig
I got
$$A_g=(\pi - \frac{\theta}{2})\cdot (50)^2 + \frac{\theta}{2}(50-10\sqrt{10})^2$$
where $$\theta=\arctan({\frac{30}{10}})$$
what did u get?
Lol
@tropic stirrup what's it supposed to look like
Eh hold on lemme draw
oke
"The rope is fasted to a hook ... 10 meters from the corner[vertex] and on the longest side"
This is very vague
Usually in geometry side is restricted to a line segment
oh
owo sum of quads
ya for some reason i thought "on the longest side" meant to extend the line
so the hook would be on the extended line
thank you @tropic stirrup
That could describe a few things. Can you provide more context?
Alright.
So, think of it this way. If A,B, and C are collinear, then they're on the same line.
yea
Awesome.
So the ratio tells you that the distance between B and C is twice as long as the distance between A and B. Still good?
yea
Good deal. Since you have A and B, you can come up with a right triangle whose sides are $$\Delta x$$, $$\Delta y$$ and $$\sqrt{\Delta x^2+\Delta y^2}$$, right? This is $$\Delta ABD$$ where $$D$$ is the point that completes this right triangle. Does this much make sense?
i guess
Cool. There's another triangle $$\Delta ACE$$ which is similar to the first. In order to scale $$\Delta ABD$$ up to $$\Delta ACE$$ we have to recognize that the hypotenuse of $$\Delta ACE$$ is 3 times the size of the hypotenuse of $$\Delta ABD$$ because in order to have a ratio of 1:2 on the same line, the line must be made of 3 equal segments.
Still with me?
yea
oh
can i find the slope
of that one small triangle
then do it 3 times
adding
That's almost what to do. What we really want to do, though is to find $$\Delta x$$ and $$\Delta y$$ so that we can compute $$3\Delta x$$ and $$3\Delta y$$ because $$C_x = A_x+3\Delta x$$ and $$C_y = A_y+3\Delta y$$
ok
Are you alright here, or should I keep going?
idk
Give it a shot from here, and then come back. ^^
Remember to draw pictures! They help a lot.
the horizontal component of AC is -15 units
๐ฑ
so that of AB is -3 units
the vertical component of AC is 5 units so that of AB is 1
idk how to explain it better
try drawing it
ok
calculating the slope isn't a very direct way of solving it
A-B is (4,8)-(7,2) = (-3,6)
is that what you meant?
yea
okay now what's B-C?
no idea
whenever you get something you don't know, use variables!
let's say C = (x,y)
now what's B-C again?
7,2-x,y
wat
can you solve it from there?
did you follow until (-3,6)/(7-x, 2-y) = 3/2 ?
i cant remember that equation
read the process then
and you realize that the problem is telling you that (A-B) / (B-C) = 3/2
you're just flustered for some reason
There's another way.
First, 3/2 is 3:2
That's one thing to note.
To say that the ratio between $$\overline{AB}:\overline{BC}$$ is 3:2 is the same as saying that the lengths of the the lines are related like this: $$3\overline{AB}=2\overline{BC}$$. Does this make sense so far?
yeanvm im done
Are you sure?
i dont get it
[pkk
p[]
i gave up ont hat one
im doing this one now
now this one acutally makes no fucking snese
i drew it out
and gave me 2 different slopes
uiovbhuio
I remember doing something like that when I was a bit younger.
i remember this too lol.
wat does locus of a point mean?
I made it to what I think is halfway done with the problem but I got stuck
I tried making triangles out of the parts not including the inner rhombus but I still have too many variables
Iโll show a screenshot of my work if necessary, unless thereโs no point because thereโs a better method
Hi
bd*ac/2 = 24
it is 60,120,60,120
therefore the inside rhombus is the same
Split the inside rhombus into 2 triangles
U get 60,60,60
so 2* s^2 * root3/4
bd*ac = 48
Df is scaled down 1/2
For each side
So it's db*ef = 12
So area is 6
Prob wrong
@waxen gorge i got 8
Seems legit enough :p
idk if my reasoning is legit
but we can split up the shape like this
so the smaller one has 1/3 the size of the larger?
How do you know the scale factor of the inner rhombus?
there's two parts inside the smaller rhombus, and 6 in the larger one?
because ABCD is a rhombus, we know that AD = AB
so <ABD = <ADB
since <BAD = 60 ADB is an equilateral triangle
similarly BCD is an equilateral triangle
you can do a load of triangle congruence stuff, turns out all those triangles drawn in are congruent, which means they have the same area
if diagonals of a quadrilateral is congruent, is it enough to prove that the quadrilateral is a rectangle
No
can someone help me quickly
how do i find X
I don't really understand geometric means
pythagoras theorem
for both the top and bottom triangles
you can notice that they're similar triangles too
that makes life easier
these won't help
just apply triangle similarity
and fill in whatever information you get
try that and show me
your similarity is a bit off
8/17 = x/15
those are the two corresponding sides
or like 8/x = 17/15 maybe is more clear
because 8 and x are the similar sides
and 17 and 15 too
oh that makes sense now
hmm so it's 120/17
@neon fossil
i have another question man im sorry xd
is this right xd
i dont think i can write that here haha xd
Can someone make me an easy refrence sheet for all congruence postulates?
For prooving angles and shit
I'm talking about like, definiton of congruence and substitution property of equality and shit
Yeah that too
The reasons for proofs
And examples of what they look like next to them
Yeah. I would really appriciate it though.
So like every thing that proves congruence
The only other option is skimming through all 70 of my lessons to find them and then forget by the time the next test comes around and have to do it again
Stuff like this
I'm confused
Well, not really that confused
But I want to know why sin, cos, and tan are used as trig functions, as a proof
How can we demonstrate that if two right segments meet in the middle then they form a parallelogram?
can you rephrase that?
is 7 a triangle idk how to do this
idk how to do nine
whats 8 just curious
no clue, doing odds
yes
i know that, but how do you find the number of sides
if im given the sum of interior angles
Kek
nitro
whats nitro
i took a video of my girlfriend
nope
oh my god i hate math
how u get that equation 180(n-2)
number nine
LOL
aaaaaaaaaaaaa
is it 7
for number 9 it would be yes
what the fuck do i do
haha i guessed
u can easily derive it
lol
by slicing a polygon into triangles
if a square can be sliced into 2 triangles and a pentagon can be sliced into 3 triangles
straightaway theres a noticeable pattern u can work on with
ya
k just clarifying
uhhhhh
do i do like the sum of all these angles = to N if n is the number of sides?
like i dont know what to do
@runic jackal
wait cant u just do 3x+2x+110+86+64=540
no
i dont htink so
i did the sum of all interior angles = 180(n)
it sounds right
so i did it
confusing
THIS IS WORSE
IM NOT DOING THOSE
im outta here
^ i stil need hepl on me problem
prove area of R1 = R2?
they have the same length for their bases
and have common heights
Steps 26^2 times 22^2 minus 2 times 26 times 22
Which was 16
Then cos(72) times 16
Which was 5
im not sure
sozz
but that doesn seem right cuz its an acute triangle and since one angle measure is 72, then the sides should be realitively similar in number
but 5 seems kinda like a distant number
I got 4.94427191
@ a helper
But rounded it to 5
Anyone know what this is asking? (t is theta)
Either they mean cut it into 8 equal slices, in which case 8
or they mean lengths, in which case 1
or they mean coterminal angles which is infinity
๐
8 prob
x, probably.
okay
let's split the shape into a rectangle which has area (2x+10)(x+5) and the triangle
we know the diagonal length, as well as the height
and we can find the base using pythagoras
what will the base be?
how?
i drew it, and i labeled each angle
i put w = x+50, but idk where to go from here
Is that a rhomboid
Fuck forgot what they are called lol
4 sides, that are two by two parallel
In case it is one
no just parallelagram
Then you know that the acute angle + phat one = 180
or however you spell
Ye that one
yeah, i got it
but will you help me with these next few
:)
i am really bad at math
i got 12
kuje'
Wut
You also know that the intersection of the diagonals cuts them in half
Aka is a midpoint
yeah
So DE=BE and AE=EC
