#geometry-and-trigonometry
1 messages ยท Page 157 of 1
Mhm
it is similar because all the angles are equal
Because the two sides are scalable and the angles are the same, it's similar
and the sides follow a proportion
It says if they are, write a similarity statement and give the scale factor
if you multiply to sides of the small one by 1.2, you get the big one
scale factor = 1.2
statement: Triangle VUW ~ Triangle SRT
Ok thanks for explaining the whole process. And around that time got me confuse. So while you guys were explaining had to to take some notes and write something down on my paper.
=tex \frac{18}{15}=\frac{12}{10}\text{ and }32=32\therefore\Delta VUW \sim \Delta SRT\therefore\text{ The two triangles are similar.}
No problemo
btw, those three dots are therefore, you'll need to use it a lot so be warned :p
Isnt the 3 dots look like a triangle?
Yea
Oh ok
Thx for helping on number 7 and thanks to asian doge for helping me too. It helped alot the way you two explain well.
And I got another question I need help with too.
Ima send pic
mk
@shy shale same technique my friend
Thats different
Find the ratio of corressponding sides
if they are equal they are similar
if not then no
i havent done the calculations yet
but that's the method
i dont know, did you calculate it?
Im trying
OH
It's just asking you to prove the next two things are similar in the same manner as above ;p
Same as 7 I think, do the math
Whys it not similar?
Do you understand what it means for two shapes to be similar?
Cause their the same shape that are similar meaning equal sides of the angles???
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Ok
and corresponding angles are equal..
Alright
21.6/4.68 โ 9/1.8
If the corresponding sides are equal, the corresponding angles must also be equal
not similar
=tex \frac{QR}{VT}\neq\frac{RS}{TU}\therefore\Delta QRS \not\sim \Delta UVT
the ratios are not consistent
except it uses squiggly lines instead of straight ones at the end, I just forget the symbol
yeh there u go dromas
there u go mate
But I encourage you to think why this is actually so, because it will help a lot in later places.
Ok thanks bro. Hope it actually does help for the near future to.
too* lol ๐ ๐
๐ค
Oh lol
lel
What if there's two near futures? ๐ฎ
@crude kraken what maths are you in
This is too confusing D:
According to my transcript, pre-calc
but I'm studying stuff ahead :p
Omg lol boi we are in the year of 2017
so I'm in some sort of mix of precal and cal
So I guess the future is after 2020 somewhere around their or after the year of 2030?
Idk
@crude kraken high-five im in precal too, what grade u in?
11
Damn you one grade ahead of me
oh you're literally 12
Im in 10th grade a sophomore
In high school
Oh also I need help with a ither question too
Alright
@shy shale actually im 4 grades ahead of u, since u r a soph in geoemtry, im a freshman in precal
Need help
man samething
Well what im guessing it is similar
Since the the triangles are vertical angles
Of the V and the teacher told me about it
So is it similar?
@upper karma @crude kraken
they are similar yes
but if not, then not enough information given
Oh yay was right it is similar
there is enough info....
but I have absolutely no clue what theorem says "Two lines in a plane crossing are symmetrical goddamnit, and becasue the angles are the same across ways teh triangles must be similar"
given 2 equal angles, u can figure the other one out by vertical angle
therefore similar by AA
Also need to write a similarity statememt and postulate of theorem
Ok angle angle
@upper karma
So how would I write it for the statement
Nvm dude someone is helping me in the other discord server on homework help
๐ฆ ok
I was just asking where was everyone at? Cause I was afraid this channel might go dead since no was talking.
this is quiet if Sev and Ann arent here
@DromasGamerHD#3722 get you state it by either brackets or use the word "by"
do what your teacher ask u to do
Did I calculate this area right?
does anyone know any interesting uses of hyperbolic geometry in real life?
thanks
@crude kraken Is that a Limacon?
it's a cardioid
This equation gives a hyperbola, right?
yes
k, thx. Thats all I needed. Was on my phone and maths came up.
ill disappear back into the shadows. bye.
=wolf plot y^2-x^2=1
Query made by @white swift
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+y^2-x^2%3D1
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/
๐ค
Three planar regions A,B,C partially overlap each other, with |A|=90, |B|=90, |C|=60 and |AuBuC|=100, where |โข| denotes the area. Find the minimum possible |AnBnC|.
Can anyone help me with this
The midpoints of the sides of a triangle are (5, 4), (8, 5), and (6, 0). Find the coordinates of teh vertices of the triangle.
what have you tried so far?
@thick coyote isn't it just be 40?
well, for the union to be 100, then the intersection of one 90 and the 60 has to be either 60 or 50, and 50 is a smaller number
so then you tack on the other 90, and align it so it drops it down to 40
Is sin(x) the same as $$sin(\theta)$$?
Ok, I was just thinking that XD
i mean they're the same function, just with different variables as arguments
the function is still sin()
im confused on 34
it is
ik u cant read it
So, we take Triangle ADB and find AD
u can use Pythagorean theorem for the right triangle 5-?-13
then use the ? to figure out the length of x in the x-?-20 triangle
ยฏ_(ใ)_/ยฏ
i did $$13^2+(x+5)^2=20^2$$?
oh be careful :o
?
do u have a right angle for that :o
Aight.
no
o yea for some reason i thought x was DC not EC
so u use Pythagorean theorem twice is what im getting
ya
ok
x=11
i thought it way to much XD
i thought to use the equation up there
3 problems left and they only ask for perimeter and area XD
Nice.
?
== sqrt(80)
8.94427191
sqrt5 ?
ye
=tex \sqrt5
looks impossible to me
it is possible
its equillateral ๐ค
no
what do u call them ๐ข
isosceles
two-side-equal
okay so if the top vertex is A, the base is BC from left to right, and that height is BH
that's the one
is the base then 10 and 5?
oh
I have problem here. Triangle edge lenghts are
a=39
b=20
c=45
I have to calculate bisectrix(bisector)
what formula i have to use and could someone explain it please?
bisectrix faces to edge a
it's angle bisector
hey! thanks!
No problemo ^^;
@tropic stirrup one question. what are those lines above formula?
Oh it just means "segment"
in here the line segment itself and its length are both expressed by the lines above the letters
because i think that in my school we learn it somehow differently but i might be wrong
Nah it's just the difference of notation
because i have never heard of Stewarts theorem
okay i will keep that in mind
The proof of it can be searched easily through the internet
i know
Uses Pythagorean
which grade usualy learn this theorem if you know
5th
in usa?!
Dunno, I just learnt it by myself
i go in 10th
And nah that's a lie over a cake
im from europe btw
American math is slow
Don't worry
ohh i remember something about this. i think teacher taught us this theorem but didn't call it steward's
ok bye
How can you tell if a slope is positive or negative? Am I looking at the picture to determine that or the answer?
Is the slope going up or down? What was the original question
You mean find the slope of the line connecting (0, 0) and (9, 3)?
m = rise / run
m = difference in y / difference in x
m = (3 - 0) / (9 - 0)
m = 3/9 = 1/3
Yes, I know how to find slope.
I just need to determine if that's a negative slope or a positive slope.
Am I looking at the actual answer to see if that's positive or negative?
Well, 1/3 is a positive number
Or am I looking at the line on the graph?
So we have a positive slope
ah thanks
So, for (-6, 0) and (0, -3), I would be getting a negative slope?
Since the slope is a negative number?
ya
i get no answers in #help-1 so i'll ask here :
here's the pb :
You have to set 5 points to build an elliptic function of [-5;4] interval:
- at 0,0
- at 31,2
- with x at 127 and u have to find y
The 2 other points so that the function has the 31,2 point as maxima (Those points will have a x<0 & y<0)
And the sum of all entire x from 0 to 127 included has to be at -128
What's the quadratic formula of this function ?
christ, inserting notation right in the middle of a sentence
I forgot what alt., con., and int. are short for
corresponding
con, not corr
exactly why i need help with it lol
I mean, i get the logic behind the math and everything and can do it when its in like basic terms
but not this
you get the hang of the terms by practicing
except these are overly fancy
Hey guys,
DC = 12 cm
AB = 6 cm
AD = 8 cm
ABCD is a trapeze
AB || DC
And the distance between AB to DC is 8 cm
* I proved that triangle AEB similar to triangle DEC
I need to find ABCD's size, how to?
I don't know that AD is height
@final prairie ืื
ืืฉ ื ืืกืื ืืฉืื ืฉื ืืจืคื
ืืืืื ืืคืื ืกืืื ืืืกืืกืื ืืืงื ืฉืชืืื
ืื ืืืืื ืื ืืื 8 ืื ืืืืข ืฉืื ืืจืคื
ืืืกืืกืื ืื 6 ื-12
ืื ืืืฉ ืื
ืืชื ืื ืืืืข ืฉ8 ืื ืืืืื
ืชืืืจืชืืช ืื ืื
ืืื ืื ืืืฉืคื
ืฉืื ื ืืืื
AD ืืืื
ืื ABCD ืืจืคื ื AB||DC ืื AD ืืื ืืืื
ืื ืืืืจื
ืื ืจืืข
ืืื ืชื ืื ืืชื ืืืืจืจ
ืื? ๐ @final prairie
ืืื ืขืื ื ืชืื ืื?
ืื ื ืืฉืื ืื ืื ืืชื ืืืืข ืขืืจืืช ืืงื
@west dune ืื ืืื ืชื ืขืืฉืื
ืืืงืื
ืดืืืจืืง ืืื ืืืกืืกืืืด ืื ืืขืฆื ืืืืื
ืืื ืื ืืงืฉื ืฉืื ืฉื ืืืจืคื
ืืฉ ืื ืืฉืคื ืืื?
ืืฉืืืืจืื ืดืืจืืงืด ืืื ืฉืชื ืืฉืจืื ืื ืืขืฆื ืืืจืืง ืืื ืงืฆืจ, ืฉืื ืืืืื
ืืื ืืฉืคื ืื ืืืืจื
ืื ืืืจ ืืืชืจ ืืื ืช ืื ืงืจื ืืคืืื
ืื ืฉืื ืืืจืคื ืื ืฉืชื ืฉื ืืืช
ืืื ืืืชืจ ืงืฉื ืื ืฉืื ืืืฉืืืฉืื
ืื ืืื ืื ื ืื ืืืื ืืืืืื ืฉ
AD
DCืื ื ื```
ืืื ืืฉืคื
ื ืืื
ืืชื ืื ืื ืฆืจืื
ืืชื ืจืง ืฆืจืื ืืช ืืืืื
ืืืื ื ืชืื
ืื ืื ืชืืืง ืืช ืืกืืืื ืฉืื ืฉ AD=8
ืื ืืชื ืื ืืืืข ืฉืืื ืืืื
?
ืกืืื ืช AD=8cm
ืื?
ืื ืื ื ืืื
ืื ืืชื ืืืืข ืฉืืืืื ืืื 8
ืืชื ืื ืืืืข ืฉAD ืืืื
ืืืงืื
=tex 8(12+6)/2=4*18=72
?ืืจืืง ืืื ืืงืืืืื ืืื ืื ืืืืื
ืื ืืื ืช ืื ืงืจื, ืืืืื ืดืืจืืงืด ืื ืคืฉืื ืืืจื ืืืืื
ืืืืชืจ ืืฆืืื
ืชืืชืื ืดืืืจืืง ืืื ืื ืืืืื, ืฉื ืชืื ืฉืืื 8ืด
ืฉื ืื ื ืืืืขืื ืฉืืชืืืืงื ืื ื ืืฉื ืืชืืื ืื ืื ืฉืืชื ืืืงืฉ ืขืืจื ืฆืจืื ืืืชืืื ืืืชืื
ืืืืคืฉืจ ืกืชื ืืจืฉืื ืืืจืื ืืืืืืืช
ืืื ืชืืื, ืืื ืชื ืืืชื
ืื ื ืืฆืืจื ืขืืจื ืืขืื ืืฉืื ืืืจื ืื
ืืืจืืง ืืื ืฉืชื ืืฉืจืื ืืื ืืืจื ืืืืื
ืื ืืกืื ืฉืืื ืงืฆืช ืืจื ืคืฉืื, ืื ืกืชื ืืฉืืื ืืืืื
ืืชื ืขืืฉืื ืื ืฆืจืื ืืืฉื ืืช ืฉืืื ืืืฉืืืฉืื
Oriented shit
Like we like to call it when programming ๐
ืืื ืฉืชื ืืฉืจืื ืืงืืืืื **
ืื
ืืืฉืืช ืืช ืืืก ืืืืืื ืืืฉืืืฉืื?
'ืืงื, ืื ื ืจืง ืกืืืืชื ืืช ื
ืื ื ืืืื ืืืืื ืืื ืืคืชืืจ ืืื ืืืืืื ืืช ืืฉืืื ืืืฉืจ ืืจืืฅ ืืคืชืืจ
Take your time :p
:}
ืื
ืื ื ืืืื ืืืื ืืงืืช
ืื @ ืื ืืชื ืฆืจืื ืขืื ืืฉืื
Wait, Hebrew is also written right to left? :o
Yes, It's the first language in histroy to be written RTL.
Now I did not know that
A day without learning something new is a wasted day @hard atlas
True ๐
ืื... ืืืืืง ืืืงืชื ืื ืืชืืืจืช
๐
ืืฉ ืื ืืืืืื ื ืืื
ืื
ืฉืื ืืืฉืืื ืืืขืื ืื ื ืฆืจืื ืขืืจื ืืืฉืื ืืืจ ๐ฌ
ืืกืชืืจืช? ืื
jesus fuck
ืืื
ืื ืืื ืงื ืื ืื ืืื
EOC = EDO ืืื ืื ืื
EDC=90ยบ
ื ืืื
ืืืงื ืื ืืื
ื ืืื ืืฉ ืืฉืคื ืฉืืืืจ ืฉืื ืฉืชื ืืฉืจืื ืืงืืืืื ืื ืื ืฉืชื ืืฉืืืฉืื ืขื ืืืชื ืืกืืก ืขื ืืื ืืื ืื ืงืืื ืขื ืืฉื ื ืื ืฉืืื ืฉืื?
ืืืืข ืื ืืคืืื ืืืชืจ ืคืฉืื
ื ืคืืช ืืื ืื ื ืจืื ืื
ืื ื ืืืืข ืืื ืืฉ ืื ืืจืืง
ืืืงืื
ืื
ืื ืืฉ ืืื ืืกืืก ืืืืื ืืฉืืชืฃ
ืื ืืื
ืชืืกืืจ SโEOP
ืืฉืชืืื
ืืงืืืืช OPC=EPO
ืืืกืืจ ืืืืื ืฉืืืื ืืืืืื ืฉืืืื ื ืืชื ืืืืื ืฉืืืื?
ืจืืข ืื
=tex a=b\implies a-c=b-c
Np
ืืื ืฉืืฉ ืืช ืืฉืจืช ืืื ืขื ืื ืฉืื ืฉืืืื ืื ืืขืืืจ
Yep
ืืฉ ืื ืขืื ืืืืืืืจืื?
ืื ืื ื ืื ืกืืื ืืืืืืืจืื ืื
ืืื ืืื ืื ื ืืืืื ืฉ
EOC = EOD
ืชืืืจืชืืช ืื ื ืืืืข ืืื ืืื ืืขืฉืืช ืืืืืื ืื ืื ื ืืฆืืจื ืืจืฉืื
?ืืืฉืื ืื ืกืืื ืืืืืืืจืื ืืืืื ื
ืืฉ ืืื ืืกืืก ืืฉืืชืฃ
EO
ืืืฉ ืืื ืืช ืืืชื ืืืืื
ืืื ืืฉ ืืื ืืืชื ืืฉืื
ืืืืื ืฉื ืฉืชืืื ED
ืื ืื ื ืคืฉืื ืืจืฉืื ืืืฉืคื
ืืฉืืืฉืื ืืขืื ืืกืืก ืืฉืืชืฃ ืืืืื ืืื ืื ืฉืืื ืฉืื
ืืื ืื ื ืืืื ืืืืื ืืืื :p
ืืื, ืชืืื
ืืชืืืื
ืชืืื ืื
๐
ืื ืื ืืืจื ืฉ
DC || EO
ืืื ื ืืชื ืืืืืื ืืืช ืืขืืจืช
ืฉื ื ืืฉืจืื ืืืงืืืืื ืืืฉืจ ืฉืืืฉื ืืงืืืืื ืืื ืื
ืืกืืจ ืื
ืืจื ืืืืืืืืช ืงืืจืืื ืืื ืืจื ืืื
If $$AB||CD$$ and $$CD||EF$$ then $$AB||EF$$
Right triangle sides are a=18 b=24 c=30
And i have to calculate narrow-angle bisector lenght.
what formula do i have to use, if i have to?
looks like this
is the 18/30 angle split in half?
yes and 24/30
yes of course
are you sure?
tell me the answer
ok one is 9โ5 and other one is 8โ10
I got 8 root 10
you got it?
square root of 657 is what i got ๐ฆ
And I used cosine formula
i have to find that formula then probs.
cool
so
hey I need help
wait Dromas
I need 3 more questions to finish
angle d = 47
Theย cosineย rule. We can use thecosine formulaย to find the length of a side or size of an angle. For a triangle with sides a,b and c and angles A, B and C theย cosineย rule can be written as: a2ย = b2ย + c2ย - 2bcย cosย A.
@sudden helm
WHAT?
COSINE FORMULA?
WE DONT HAVE ANGLE DOE
we can inverse it
fuck
i forgot
@upper karma thanks!
We don't need the angle
Post the question dromas
y = 180 - 90 - 47
i told him
ok
as it is that triangle
do you understand why?
dromas
so angle C is parralel to Angle B
so angle C = angle B
ok I have that
so its not 43?
It is 43
you going to have to read it
i cant see it
What have you tried?
i cant see a damn word in 45
can you read 35
35*
What have you tried so far?
trying to think
there
their took a picture side ways
like can you explain how to get to the answer, cause I don't understand how to do number 35
a. โ10?
no
I will show you
ok
U know basic trigonometry? Dromas?
You don't need trigonometry
How?
am i seeing it incorrectly
I did it correctly
Ik but I'm using trigonometry and that's easier that way IMO
so when you input the numbers I do cross multiply to find my answer?
You need to imput values first
ok
What is length DC and what is length BC?
Hence , โ10.....๐
But he does not know trigonometry
archytext
It is better to do it this way
look
yeah
i this far
Call the unknown value x
x^2 = 10
Also , I used tantheta and u used similarity , same idea on both our approaches , almax
when I square root 10 I get 3.16227766
I don't remember similarity now , so used tantheta
Yes
you can just write it as sqrt(10)
^
The angle at home
Do you know the formula for volume of sphere?
PiR^2 is volume
pir^2 is area
=tex 4/3pir^3
I think its that
shit
so how I do it
=tex \frac{4}{3}\pir^3
Rendering failed. Check your code. You can edit your existing message if needed.
=tex \frac {4ฯ}{3}4^3
=tex \frac{4}{3}\pi r^3
Having a hard time with latex
You just plug in the radius into the formula
And solve
=calc (4pi/3) * 4^3
Failed to parse equation: Invalid syntax at position 2
(4ฯ/3) * 4^3
^
like that?
Yeah
=calc (4pi/3)*64
Failed to parse equation: Invalid syntax at position 2
(4pi/3)*64
^
You'll get the answer in cm^3 . Just remember
dam
for 4 to the third I get 64
:/
for 64 Do I times 4 and divide it by 3 and times pie?
oh ok I got got it
Ahha I don't remember conversions
1 m = 10dm = 100 cm
had to calculate it
1m^3 = 1000dm = 1000000cm^3
pretty sure im correct
Can someone explain the difference between a parabola and a hyperbola
a hyperbola has asymptotes
a parabola doesn't
but also: a parabola is the locus of all points equidistant from a focus and a directrix (line)
a hyperbola is the locus of all points such that the difference in distances from each point on the hyperbola to the two foci is constant
a parabola has no asymptotes and only has one arm
By that image, the hyperbola does as well
Hi, i found some solution to my pb
but i need ur help
Here's my function : A abs((B ln(C x + D)) / (x + E)) - F
I get this kind of courb :
how to make the maxima a little more at right plz ?
(A to F are constants)
i want to shift the courb to the right
but if i do it directly, i get no values at little abscissas
uhmmm does A abs((B ln(C (x-1) + D)) / ((x-1) + E)) - F
not work?
or something like that?
x+1, not -1
oh ok
I dont know what is happenin in that case then ๐คท
it's resolved now ^^
i dont understand number 9
what is radical form ๐ค
=tex \sqrt(x)
o yes right
radical as in sqrt
its isoceles ๐ค
have you done trigonometry? ๐ค
no, im not in trig yet
=tex \sqrt{x}
@past mantle
anyway
these are all isosceles right triangles
their sides are in the ratio 1 : 1 : sqrt(2)
maybe since its a 45-45-90 triangle, maybe $$15 = l\sqrt{x}$$
\sqrt{x}
i got $$\frac{15\sqrt{2}}{2}$$
which one?
is that right?
9?
for 9
yeah
backslashes!
We don't know what's the data which were given
I need to count the area of A
Again... give us the question's data
uhm
do u mean i should translate the question
sorry im not a native speaker but I can translate it if thats what you mean
So translate please
So the quadrilateral is divided to four pieces by drawing diagonals. Three areas of the pieces have been marked. Count the area of the fourth piece A
Tell me if you cant understand
hey
Iโm here
But firsy
*first
I need your help to label all vertices on that diagram
Including the intersection of the diagonals
Just to make it easier to communicate
Uhm
Label whatever way you want
just a sec
Take your time
Whats the fifth
Im sorry english isnt my native language xd
Ah sorry
Yes
First, have a look at triangles ABE and CBE
mkay
They share the same perpendicular height dropped from B
yes
(Itโs not the same line as BC by the way. Letโs call it BH)
yeah
Then area = 1/2รheightรbase
So Area of ABE = 1/2รAEรBH
Area of CBE = 1/2รCEรBH
In other words,
Im still with you ๐
=tex \frac{\text{Area of ABE}}{\text{Area of CBE}} = \frac{AE}{CE}
Oh hey it worked
thats noice
So now you can find AE/CE
The ratio
Now, by the same logic,
=tex \frac{\text{Area of ADE}}{\text{Area of CDE}} = \frac{AE}{CE}
In other words,
=tex \frac{\text{Area of ABE}}{\text{Area of CBE}} = \frac{\text{Area of ADE}}{\text{Area of CDE}}
ill try to get the answer
Itโs just calculator work
It is
dont say it ๐
Glad I could help
So I went to tutoring today after school and the teacher was helping me for geometry before the test
And it helped
If there is a 45-45-90 triangle, is the hyponeuse $$l\sqrt{2}$$
if anyone needs like help in physics, chemistry, biology, etc lmk
hi guys
im a freshman and im taking Honors Geometry
can any1 help me understand rotations on a coordinate plane and how a-(a-c)=2a-c
a - (a - c)
= a - a + c
= c
It doesn't
lies
i hate geometry so much ngl lol
lol
I like how your grader drew clouds over the incorrect parts
Lol
random question: when you're adding segments are you supposed to put the bar thingy on top?
if anyone needs help in calculus/or math in general i can help(edited)
im on a lot these days
but please PM me tho, im in so many channels i forget to come here
just wanna help since my projects are finished ๐
but if someone can answer for them that works for you but if you see me online shoot me a question
@dark sparrow like Segment AB=Segment AC+CB
Do you do AB=AC+CB or actually put the line on top
do you mean vectors?
bc if you're talking about segment lengths then that's only true when C is between A and B
anyway... notation
ffhh
i'd prob put an arrow over them
it's a bit of a bitch to TeX but
=tex \overrightarrow{AC} + \overrightarrow{CB} = \overrightarrow{AB}
@dark sparrow Isn't that for rays tho?
I meant the arrow thingy above the letters
ok
I came up with my own question:
Show that the sum of two gradients A and B, is: https://prnt.sc/hi9tde
for example, shown in this picture: https://prnt.sc/hi965n
You can see that the gradient of the original blue line is 1/2 and of the red line is 1/3
You can see that the new blue line has a gradient of 1 which is (1/2 + 1/3)/(1-(1/2)(1/3))
Am I overlooking any simple solutions to this?
=tex \tan(x+y) = \frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)}
that's the intended solution, yes, by converting the gradients to angles such that tan(x) = A and tan(y) = B so x and y are the angles so tan(x + y) gives you the gradient of the new line
but is there anything simpler, eg no trig?
Let complex numbers P, Q be P =a + bi, Q = c+di. (P)(Q) will have angle = sum of the angles of P and Q.
PQ = (ac -bd) + (ad + bc)i
Slope of PQ = (ad+bc)/(ac-bd) = (d/c + b/a)/(1-(b/a)(d/c)) Voila.
=tex P = a + bi, Q = c + di
\ (P)(Q) = (ac - bd) + (ad + bc)i
\ m = \frac{ad+bc}{ac-bd} = \frac{ad+bc}{ac-bd}\cdot\frac{1/ac}{1/ac}
\ = \frac{d/c+b/a}{1-(b/a)(d/c)} = \frac{b/a + d/c}{1-(b/a)(d/c)}
Well
You can determine the internal angle
Since all internal angles are equal and angle sum
And then x is 180 - internal angle
Since angles on a straight line
Though
I'm pretty sure you can also just divide 360 by 5
@thorn talon I thought he said 30
i can't read
Xd
whoops