Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/2` and the angle between sides B and C is `pi/12`. If side B has a length of 22, what is the area of the triangle?

Answer 1

Area of the rt. triangle `color(maroon)(A_t = (1/2) * a * b = 64.9 " sq units"`

Explanation:

`b = 22, hat A = pi/12, hat C = pi/2`

`hat B = pi - hat A - hat CC = pi - pi/12 - pi/2 = (5pi)/12`

Applying Law of sines,

`a / sin A = b / sin B = c / sin C`

`a = (b sin A) / sin B = (22 * sin (pi/12)) / sin ((5pi)/12) = 5.9`

It's a right triangle with `hat C = pi/2`

Hence area of the rt. triangle `A_t = (1/2) * a * b = (1/2) * 5.9 * 22 = 64.9 " sq units"`