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?

1 Answer
Jun 3, 2018

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#