Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/6`. If side C has a length of `15` and the angle between sides B and C is `( 5 pi)/12`, what are the lengths of sides A and B?

Answer 1

A = 15 ( `sqrt`3 + 1 ) /`sqrt`2 and B = A..

Explanation:

Sum of the angles is `pi`. So, the third angle is 5`pi`/12.
The triangle is isosceles, with A = B.
The sides are proportional to the sines of opposite angles.This gives A and B.
sin (5`pi`/12) = sin ( `pi`4 + `pi`/6 ). Expand.