A triangle has sides A, B, and C. The angle between sides A and B is $pi/3$ and the angle between sides B and C is $pi/12$ . If side B has a length of 8, what is the area of the triangle?

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Answer 1 · 2018-02-17T10:29:20

$A_t = (1/2) a b sin C =color(green)( 7.4256$

$hatA = pi/12, hatC = pi/3, b = 8$

$hatB = pi - pi/12 - pi/3 = (7pi)/12$

$a / sin A = b / sin B$

$a = (8 * sin(pi/12))/sin ((7pi)/12) = 2.1436$

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$A_t = (1/2) a b sin C = (1/2) * 2.1436 * 8 sin (pi/3) =color(green)( 7.4256$

A triangle has sides A, B, and C. The angle between sides A and B is pi/3pi/3 and the angle between sides B and C is pi/12pi/12. If side B has a length of 8, what is the area of the triangle?