#geometry-and-trigonometry
1 messages · Page 167 of 1
You can construct 6 triangles in that shape. Each of them have an angle π/6 from the side. So, we can split this triangle in half and use trig for the apothem
tan(π/6) = a / 1.5
a = 3/2 tan(π/6)
a = sqrt(3)/2
Oh. Then 30 degrees. 180/6
=tex tanx/-tan^2(x)
how do u simplify this
What's u/u²?
ye
How do you do this?
The length of one base of a trapezoid is 19 meters and the length of the median is 23 meters. Find the length of the other base in meters.
ye
k
i think its 120
ok
OH
my b
plus it has to be obtuse
xD
xD
so then let me ask you, what do you have to do to find that angle?
cause i figured out my mistake
well
no urs is right
its like the step
u jsut need to keep going
ehre lemem draw it
wait
nvm
im so dumb
they wantd mnp all along
@upper karma u were right
Lol
i thoguht we were looking for mno
LOL
apologies
:3
all good haha
i went back and thought i was solving for something else hence why i thought i made a mistake
http://prntscr.com/ih4f2j I have no idea how to go about answering these
would I isolate cos or sine?
what are you given?
cos(theta)
so you would isolate that.
and you should notice that your expression will only be in terms of sine.
cos^2 = 1 - sin^2?
one more step.
yup.
and remember, since you're taking the square root, you'd have two solutions, ome positive and one negative.
but that's already covered.
I see
can you do the rest?
you know already what cosine of theta is in terms of sine.
and the denominator is in terms of sine already.
Lol
379
@waxen gorge
It has been a while 😂
It goes from one of the vertices to the midpoint of the opposite side
Oh
That statement is true for every right triabgle
What
Yeah
But it never said it was bisecting
I just came to the wrong conclusion
Ph
Oh right
But it’s not 90 degrees
Not necessarily
No
Altitudes has to be perpendicular
Really? Why
oh true
Lol
woa sotto has godlike drawing skills 👀
Yeah
How could I find their angles
😂
So it’s 45 45 90
I was right
Because the two sides are the same?
Lol
I’m not completely sure why it makes the right triangle. I get it and the drawing but not totally sure how I could explain this
😂
Yes
uωu
❤️❤️
Lol
@mint ore tag me when you're ready
ready
some of it
well, if you know that a/ sin(a)=2r
then you can figure it out
but if we dont know that:
let's mark a centre
let's call it O
i didnt know that 😮
we know cd=7
and ab=8
so let's take O and extend it to meet AB
and call this intersection M
do this similarly for O and CD; let's call that N
can you work out em?
ok i did it
okay cool
what now
what's EM?
2
nice, what's EN?
1.5
recheck
yeah
what do you mean by 'solve already'
so r is sqrt 16,25 and d is sqrt 32,5?
radius is sqrt(16.25)
but 2*sqrt(16.25) doesn't equal 32.5 -
it equals sqrt(4*16.25), see if you can understand
Hi
sinx = -.4
-.4/cosx = 9.6
cosx = -.4/9.6
cosx = -1/24
now use inverse cosx function to find x
A
@golden parrot the radius is sqrt(65/4), the diameter is sqrt(65)
@night lotus in similar shapes, corresponding sides are in the same ratio
How do I know which number goes first in the ratio?
it doesn't matter which
as long as it's the same way round when looking at equality
you don't actually have to use ratios at all, you can use fractions instead if you want
you'd get 15/20 = w/10
you could just as easily do 20/15 = 10/w or 20:15 = 10:w
it really doesn't matter
@mossy vine so w = 13 1/3?
it's 7.5?
yeah
as a rough check
it must be smaller than 10
because the 15 on that triangle is smaller than the corresponding 20 on the other triangle
ye
and y is 6?
ye, nice
okay, thank you very much
no problem 😃
AC=x+5
You just add the parts
Same works for AB
and then the proportionality is just AB propto AC
Valid hint?
oh
lemme try that
@crude kraken#219 how wouild i write out AB propto AC?
x+5 = x + 13?
However that doesn't work too well
So it's probably saying to proportionalize the two things you're given
namely
=tex \frac{x+7}{6}=\frac{5}{x}
yes ive tried that
It didn't work?
idk if i use quadratic
Query made by @crude kraken
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=factor+x^2%2B7x-30
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
👍
dilation if the scale factor is greater than 1 is called an enlargement right?
What is your x coordinate
Can someone help me with questions 28 and 29
I used coordinates to find #29 and got 122, can someone provide an easier solution?
My brain is sorta slow right now is that supposed to be a rectangle?
they don't give u lengths
I only need an explanation
the side of the square is a diagonal from the midpoint of the rectangle to and edge
how do you know C is the mid point?
i dont 😮
👀
i see similarity tho :/
ead
cdg
feh
meh whatev june can do it .-.
june knows everything
h.
i think.
ya.
but anyway.
hfe and cdg are congruent.
so their areas must be equal.
cbh and dea are also congruent.
so their areas are equal too.
now look at the figure and this:
arCDAB + arCGD + arCBH = arFGDE + arEAD + arFHE = total area of the figure.
arCGD = arFHE.
so.
arCDAB + arCBH = arFGDE + arEAD.
so you basically need to prove that arCBH = arEAD.
okay thxs
but you know that's already true bc they are congruent.
therefore, arCDAB = arFGDE.
which is what you needed to prove.
how would u solve for 29? I did it with coordinates and it got messy even though I am correct
is there an easier way?
im just lost
like
he doesnt tell us how to do this
and i want to die
im assuming its a lot of slope and distance formula?
Not really
First check if x and y spacing are the same
Then check if their differences are the same
Then I guess u can sketch if it fails both
you're back
so to prove its a rectangle, you need opposite uh
whats that word called
recip something
To prove its a rectangle make the slopes opposite reciprocals
parallels?
idk if im even right
ya
oh that yeah
what PJS said
so unless i did my math awfully wrong, CB and BA arent opposite reciprocals
Let's see 2-5/-7-6
well
-3/-13
well i did it wrong already lol
Yep
Yep
Yeah a square and rectangle all have 90 degree angles
i just know a square is a rectangle but a rectangle isnt a square
oh yeah
im a bit mental sometimes
and since they arent opposite reciprocals it eliminates both of those
so it has to be just a regular quadrilateral, or a parallelogram
now we can try to see if its a trapezoid maybe, or a parallelogram
or that
yeah
so a trapezoid is one set of parallel sides, and one set of congruent sides right
Well, you see if, the opposite sides have the same slope
Okay so how did you prove that?
well
i found the slopes of CD and AB
not the same
so its either a trapezoid, iscoc trap, quadrilateral, or none
DC = -4-2/-5-(-7) = -6/2 = -3
DA = -4-(-1)/-5-8 = -3/-13
You got the equation right
But we can see that AB and DC have equal slopes
and CB and DC have equal slopes
well i have to say what type of parallelogram it is
i would think its a rhombus right?
because sides are equal, angles arent?
In order for it to be a rhombus all sides must be equal
so you would use the distance formula
so distance formula thats some stupid annoying stuff right there aaaa
Lol its just the pythagorean theorem lel
Yeah it is annoying
so since they're parallel
i only need to find the distance of one of the opposite sides right
For AB its sqrt(5-(-1)^2) + (6-8)^2)
So 6^2+-2^2
36+4
sqrt(40)
So in order for it to be a rhombus all sides must be sqrt(40) in length
Not necessarily
Even though they are parallel doesnt mean they have equal side lengths
like a trapezoid
so this is just a parallelogram
so yeah just a parallelogram right
From this we can say that its not a rhombus so yeah a parallelogram
okay, i know that took a long time, i have seven more of those to do
will you kindly help me out
im still barely understanding this
A rhomboid
oh
A rhomboid is the same as a rhombus but the side lengths are not equal
then how could you tell which sides are opposite?
just mental image?
anyway, number three
so it looks like a trapezoid
so we should find the bases' slopes right?
thats too complicated for me aaa
LOL just showing you what I do
oh
Anyways next question i wont use the graphing tool
i graph it
You can but you dont need to
so when i graphed this, where should we start
All you need to do is find the slopes and distances
see if the angles are 90 degrees right?
You can
so lets see AD and DC first
mkay
Yep
how do we prove if its a trapezoid?
If its a trapezoid itll have a pair of parallel sides
the bases right?
yep
so ad and bc slopes?
They have to be the same in order for it to atleast be a trapezoid
hm?
BC; -7-(-4)/13-4 = -3/9
-1/3
BA; -4-6/4-(-2) = -10/6
=-5/3
So.....
We have slopes -8/3; 1/3; -1/3; -5/3
oh okay wait nevermind
so it has to be a kite?
or wait
no
false
where do i go next
Also a kite has two pair of equal side lengths
well which sides should i check
i dont even know we never did this on a kite
aaa
i really want a new teacher
Ye
we only have a quadrilateral and a kite left right?
yep
Yep
what side is that
For BC : $$\sqrt (-7-(-4))^2 + (13-4)^2)$$
youre good
so its just a quad
Not yet
hm?
The other sides could have the same length
For CD: $$\sqrt ((-10-(-7)^2 + (4-13)^2)$$
sqrt 9 + 81
same thing?
sqrt 90?
so would that be a kite?
please say yes i dont want to do any more math
even though we have 6 more after this
and i dont just wanna not do it lol
bad ethics
you're telling me
For a kite, the diagonals must be perp.
so we dont even need to do this
NOPE lol
Haha yeah shouldve realized that
So, AC and BD must be opposite reciprocals
?
we did
oh
okay
so kite
i did my math wrong already
late
i got a 0 lol
aaaaaaaaaaa
It's not a kite
oh my god im just done with math lol
Its an irregular quadrilateral
Alright
so this looks like an easy shape
$$\frac {4-3}{3-(-2)}$$
how many points do i get taken off if i just right quadrilateral because four sides
:)
Alot prob lol
okay so how do we solve this
uh
looks like a parallelogram we're starting with opposite sides slopes
what you did was ba right
BA
1/5?
Hold on lemme see
For BC $$\frac {-1-4}{2-3}$$
-5/1
AAAAAAAAA i keep doing things wrong
-5
so opposite
Opposite reciprocals so far
so now ad and bc
DC: $$\frac {-2-(-1)}{-3-2}$$
-1/-5 = 1/5
DA: $$\frac {-2-3}{-3-(-2)}$$
-5/-1 = 5
so not opposites
damnit
wait
no opposites
im so dumb rn lol
yes
parallelogram
now i need to find if its a square or rect right
No
We showed that the slopes are not opposite reciprocals
so it cant be a square or rect
Not next lol
It can be another type of parallelogram
uhhhhh
i know all of them are congruent
so yes
???
i really dont know anymore
im dying
yes it is final answer
wait didnt we say both are congruent
i dont
even know anymore
aaaaaaaaaaaaaaaaaaaa
Hmmm hold up now im a bit confused
i meant parallel
not congruent
SO AM I
you know what my answer is
i skip this one and make my teacher do it for me tomorrow
<3
so lets do this one thanks bb
Hold on I cant quit now
damn
So yes; two sets
so it can be a parallelogram or a rhombus
use the distance formula to see if the side lengths are equal
i really really really dont want to
Test with just two side lengths and when they arent the same you can say its just a parallelogram
Hahaha
while contemplating my life choices of honors geometry
y2-y1^2 + x2-x1^2 all in square root right
yep
No no no
i really really dont want to
ill do it for you
11:00 pm
doing math homework
OH I HAVE SPANISH HOMEWORK TOO
LOOKS LIKE IM STAYING UP PRETTY LATE
BECAUSE ON QUETION TAKES LIKE THIRTY MINUTES
THANK GOD
All side lengths are the same
Nope
How do you know it has right angles?
For it to be a rectangle if the angles are opposite reciprocals
because no opposite reci
yep
you beat me to it again
Yes
however you have two pair of parallel sides
Yep
to see if its a rhombus
Yep
oh boy here we go this shit again
Im assuming you can do it
yes
Guys it's been like 2 hrs
This is not good homework
<3
ur teacher sucks
Actually u need to do CD will be enough
wait really
To proof
Because if AD is not equally to CD,it will be a parallelogram
If AD = CD, it is a rhombus
true
Nah; slopes dont matter
Because two lines with the same slope are parallel lines
for cd i got sqrt 5
what the hell
did i do wrong
oh i see
i looked at the wrong problem
shh
And you proof that it has 2 parallel lines and it doesn't have right angles, so it can be a rhombus or a parallelogram
is CD sqrt 40?
Wait
yes
THANK GOSH I DID SOMETHING RIGHT
AWAY WITH THAT PROBLEM
8 MINUTES NEW RECORD LETS GO
im going insane sorry
yep
four more
rhomboid but you havent learned that
Rhomboid...
havent learned it
yeah
This means that its either a square or rect
use distance formula to see if they are the same
Yes
Yes
Correct
yep
lol
Sure
i really dont want to do more work than i need anymore
JUST DO IT!!
yes
hehe
we dont talk about that
Kkk
we just talk about me here
because im the best
next question btw
okay, hey
will you walk me through what you do to get the slopes
oK
because i obviously dont do this right
Lol
For AB: $$\frac {-4-(-1)}{9-5}$$
@restive void Mhmm I thought u are better than us...🤔 🤔 🤔
Ok
For BC: $$\frac {-10-(-4)}{6-9}$$
cant you simplify 6/-3
so like
6/-1
i meant
3/-1
its late okay
i dont even know

yes
Yeap
DA = -5-(-1)/ 3-5
Yes
DA =2 right
yes
okay im starting to get it
Yayayayaya
so we dont have opposite recipricoles
so no square or rect
unless im absolutely fucked in the mind and messed up?
its the latter isnt it
How did you get -3
and 5/-3 is the same as -5/3
dont ask me
-10-(-4) = -6 6-9 = -3 -6/-3 = 2
reasons why i despise math - you do one thing wrong everything else is wrong
yep lol
Yes
U just need to practise more
2nd to last one
Okay you know how do to it correct?
Just write ur answer here and we will check
wait question
ab the slope will have a zero right?
how do you work with that
0/3
no?
So the slope is 0
Undefined
so how the hell do i do this
It's a straight line vertically
Sure
wait this is just a trapezoid right? one set of parallel lines?
Yeah
yeah, last one
BA: $$\frac {2-4}{-1-(-4)}$$
ye
are my slopes right - AB = -2/3 BC = 2/3 CD =2/3 AD =2/3
wait
i think i missed a negative
CD = -2/3
CD is -2/3
Yeah figured
So is this going to be a square or rectangle or rhombus?
Do it has right angles?
Uh
I see opposite reciprocals
Wait
No I don’t
So at this point a rhombus or a parallelogram right
Yes
@restive void it's been 3 hrs just sleeeeppppp