Basic trigonometry question

by MechatronO
Tags: basic, trigonometry
 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.
 HW Helper Thanks P: 5,598 What you call the Law of Cosines is actually the Law of Sines.
 P: 25 Typo. More suggestions?

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