Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/2`, the angle between sides B and C is `(5pi)/12`, and the length of B is 15, what is the area of the triangle?

Answer 1

Area of triangle `A_t = color(violet)(419.85` sq units

Explanation:

Area of triangle `A_t = (1/2) a b sin C`

Law of Sines `a / sin A = b / sin B = c / sin C`

Given : `b = 15, hat C = pi/2, hat A = (5pi)/12, hat B = pi - pi/2 - (5pi)/12 = pi/12`

It’s a right triangle and hence `A_t = (1/2) a b` as `sin C = sin (pi/2) = 1`

`a = (b sin A) / sin B = (15 * sin ((5pi)/12)) / sin (pi/12) = 55.98`

`A_t = (1/2) * 55.98 * 15 = color (violet)(419.85`