For the math-heads

MS le Roux

I'm playing around with graphing, and I'm trying to figure out the following: Draw a line from point A (0,10) to point B (100,10). Now draw a line from point B to point C, in such a way that C is below B, and angle ABC is 100 degrees. AB and BC have the same length. How do you calculate the coordinates of point C?

Shog9 0

C.x = B.x+sine(ABC-90)*BC C.y = B.y-cosine(ABC-90)*BC = C.x = 100+sine(10)*100 C.y = 10-cosine(10)*100

I think it's cool that Shog's coding johnson is longer than everyone elses -- JoeSox 10/8/03

Iain Clarke Warrior Programmer

I am assuming that ptC is just a little to the right of straight down from B. Just to check my vision of what you want is correct. ptC.x = ptB.x - |BC| cos (Theta); ptC.y = ptB.y - |BC| sin (Theta); |BC| = |AB| = 90 Theta = 100o = PI/4 + a bit. So, C = (115.63, -78.63). How's that? Iain.

Jason Henderson

AB and BC are the same length, so we can assume they are radii of a circle with the origin at (100,10). Using polar coordinates, x=radius*(Cosine(Theta)) and y=radius*(Sine(Theta)): x=(100*cos(280)+100) = 117.365 y=(100*sin(280)+10) = -88.481 Roughly. If you apply the distance formula: distance=sqrt((x2-x1)^2 + (y2-y1)^2)) distance=sqrt(17^2 + (-98)^2)=sqrt(289+9604)=99.464 Pretty close to 100.

"It is better to remain silent and be thought a fool than to open one's mouth and remove all doubt." - Abraham Lincoln

Jason Henderson
blog | articles

MS le Roux

Remind me - what does Theta represent?

Smitha Nishant

Got it all except that C.y thing. Can't figure out how you got that :-D Smitha Every person, all the events of your life, are there because you have drawn them there. What you choose to do with them is up to you. -- Richard Bach

Shog9 0

I'm assuming coordinate system where negative Y is down. Invert (10+ not 10-) for typical screen coordinates.

I think it's cool that Shog's coding johnson is longer than everyone elses -- JoeSox 10/8/03

Jason Henderson

Your answer was right.

"It is better to remain silent and be thought a fool than to open one's mouth and remove all doubt." - Abraham Lincoln

Jason Henderson
blog | articles

Shog9 0

Thanks *wanders off to find some coffee*

I think it's cool that Shog's coding johnson is longer than everyone elses -- JoeSox 10/8/03

Iain Clarke Warrior Programmer

Theta was the angle ABC. In this case, 100 degrees. Iain.

Jason Henderson

The length of BC is off by 10.

"It is better to remain silent and be thought a fool than to open one's mouth and remove all doubt." - Abraham Lincoln

Jason Henderson
blog | articles

RChin

Draw a line from point A (0,10) to point B (100,10). Now draw a line from point B to point C, in such a way that C is below B, and angle ABC is 100 degrees. AB and BC have the same length. OK, Now my solution is as follows: (NB: I haven't done any trig. maths for quite a few years, so my memory of most trig equations are a little sketchy. Forgive my pathetic excuse of a text graph :~

^
|
|

A(0,10) B(100,10)	x	D

*'''''''''''''''''''''''''''''''*''''''''''''+ -
| 100 \ 90'
| \ '
| \ '
| \ '
| \ ' y
| \ '
| \ '
| \ '
| \ '
| \ '
+-------------------------------+--------> \ '
|(0,0) 100 \'
| * C

AB = BC = 100
A<B>C = 100 deg.
~ C<B>D = 180 - 100 = 80 deg.
~ B<C>D = 180 - (90+80) = 10 deg.

since BC = 100:
y/BC = COS(B<C>D)
y/100 = COS(10);
:= y = 100 * COS(10) = 98.48

X/BC = SIN(10)
X = 100 * Sin(10) = 17.365

~ C = ( 100 + X, 10 - Y )
= (117.365, -88.48)

.QED.

(i'm sure some of you will prove me wrong) **I Dream of Absolute Zero

**

David Stone

Well, you got it right...but my question is why didn't you just use cos(80) and sin(80)

We're given this:
100
A--------------------B
θ=100° \
\
100\
\
\
\
C

Now, if we draw an imaginary triange the other way, we can say that φ=80° because of supplementary angles.
Then we can say that Cx = 100 + 100 cos(80°) and Cy = 100 sin(80°):

A--------------------B======|
θ=100° \φ=80°|
\ |
100\ |
\ |
\ |
\|
C

What's with cos and sin of 280? Where does that come from? [EDIT] Hey, if you highlight everything in the pre tags, it looks like a guy with a really long nose and a little cap on. :-D [/EDIT]

When I can talk about 64 bit processors and attract girls with my computer not my car, I'll come out of the closet. Until that time...I'm like "What's the ENTER key?" -Hockey on being a geek

David Stone

You got it right. You just went through a very roundabout way of doing it. :)

When I can talk about 64 bit processors and attract girls with my computer not my car, I'll come out of the closet. Until that time...I'm like "What's the ENTER key?" -Hockey on being a geek

Jason Henderson

David Stone wrote: What's with cos and sin of 280? Where does that come from? Think of it as a circle with the origin at 100,10 with a radius of 100. AB is 180 from BX (BX being the line from (100,10)-(200,10). When we add another 100 to get the ABC angle, that equals 280 on our circle. I haven't had trig for a while, but the polar coordinate system is pretty simple for me. For problems like this, I always try to think in terms of a circle.

"It is better to remain silent and be thought a fool than to open one's mouth and remove all doubt." - Abraham Lincoln

Jason Henderson
blog | articles

David Stone

Jason Henderson wrote: Think of it as a circle with the origin at 100,10 with a radius of 100. AB is 180 from BX (BX being the line from (100,10)-(200,10). When we add another 100 to get the ABC angle, that equals 280 on our circle. Ah, that makes sense...okay. I see your point. Jason Henderson wrote: I haven't had trig for a while, but the polar coordinate system is pretty simple for me. I use trig a lot in Physics and 3rd semester calculus. So that's why I immediately go for trig. I learned to hate polar coordinates last semester. Ever try integrating polar equations? X|

When I can talk about 64 bit processors and attract girls with my computer not my car, I'll come out of the closet. Until that time...I'm like "What's the ENTER key?" -Hockey on being a geek

RChin

I haven't done these sort of maths in YEARS! I've still got it.... :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: :jig: yeah! **I Dream of Absolute Zero

**

David Stone

Isn't math fun? :)

When I can talk about 64 bit processors and attract girls with my computer not my car, I'll come out of the closet. Until that time...I'm like "What's the ENTER key?" -Hockey on being a geek

Daniel Turini

In Portuguese, "boobies" :)

Help me dominate the world - click this link and my army will grow

Jason Henderson

Trig is all about circles. :cool: David Stone wrote: Ever try integrating polar equations? Not that I recall.

"It is better to remain silent and be thought a fool than to open one's mouth and remove all doubt." - Abraham Lincoln

Jason Henderson
blog | articles

For the math-heads

since BC = 100: y/BC = COS(B<C>D) y/100 = COS(10); := y = 100 * COS(10) = 98.48

since BC = 100: y/BC = COS(B<C>D) y/100 = COS(10); := y = 100 * COS(10) = 98.48

since BC = 100:
y/BC = COS(B<C>D)
y/100 = COS(10);
:= y = 100 * COS(10) = 98.48

since BC = 100:
y/BC = COS(B<C>D)
y/100 = COS(10);
:= y = 100 * COS(10) = 98.48