A triangle has sides A, B, and C. If the angle between sides A and B is $(5pi)/12$ , the angle between sides B and C is $pi/3$ , and the length of B is 2, what is the area of the triangle?

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Answer 1 · 2018-02-17T03:52:19

$A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366$

Given : $b = 2, hatA = pi/3, hatC = (5pi)/12$

$hatb = pi - (pi/3 + (5pi)/12) = pi/4$

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

$a = (b * sin A) / sin B = (2 * sin (pi/3)) / sin ((pi/4) = 2.4495$

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$A_t = (1/2) a b sin C$

$A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366$

A triangle has sides A, B, and C. If the angle between sides A and B is (5pi)/12(5pi)/12, the angle between sides B and C is pi/3pi/3, and the length of B is 2, what is the area of the triangle?