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?

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Answer 1 · 2018-06-03T03:36:10

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

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 $sin C = sin (pi/2) = 1$

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

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

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