Basic trigonometry question

by MechatronO
Tags: basic, trigonometry
MechatronO is offline
Feb23-14, 08:00 AM
P: 25
We got a circle with a radius R.

From a distance D from the centerpoint a line is inserted at an offset angle A1 from a line drawn though the centerpoint C of the circle, see the picture below.

I would like the are of the red triangle, provided D, R and A1.

I drew another triangle with one of its corner in the circles center for help, extracted the angle A2, got H and could then solve the problem but. However I wonder if there is a neater way than this.

What I did:

A3 = 180-A1

Law of cosines give

sin (A3) / R = (sin A4) /D

A4 = arcsin( sin(A3) * D/R ) = arcsin( sin(180-A1) * D/R)

A2 = 180 - A3 - A4 = 180 - (180-A1) - arcsin( sin(180-A1) * D/R) =

= A1 - arcsin( sin(A1)* D/R)

sin(A1) = H/R

H= R*sin(A1)

cos(A2) = (B+D)/R

B= R*cos(A2) -D

The red area = B*H/2 = (R*cos(A2)-D)*R*sin(A2)/2

And so forth. However, I get the feeling that this solution is more complicated than necessary?

EDIT: Btw the circle hasn't got much to do with the problem, but I'm just using it in a next step.
Phys.Org News Partner Mathematics news on
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
SteamKing is offline
Feb23-14, 11:05 AM
HW Helper
P: 5,598
What you call the Law of Cosines is actually the Law of Sines.
MechatronO is offline
Feb26-14, 04:22 PM
P: 25

More suggestions?

Register to reply

Related Discussions
basic trigonometry General Math 5
Basic trigonometry question regarding knee angle General Physics 5
[ HELP ] ##### Basic Trigonometry ##### Precalculus Mathematics Homework 5
Very basic trigonometry question? Introductory Physics Homework 3
Basic Trigonometry Calculus & Beyond Homework 4