A triangle has sides A, B, and C. The angle between sides A and B is $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 72, what is the area of the triangle?

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Answer 1 · 2018-06-03T09:48:24

Area of the triangle $A_t = color(crimson)(748.32)$

$hat A = pi/12,hat C = (7pi):12, hat B = pi/3, b = 72$

Law of Sines $a/sin A = b / sin B = c / sin C$

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

$a = (b sin A) / sin B = (72 * sin (pi/12)) / sin (pi/3) = 21.52$

$A_t = (1/2) * 21.52*72*sin((7pi)/12) = color(crimson)(748.32)$

A triangle has sides A, B, and C. The angle between sides A and B is (7pi)/12(7pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 72, what is the area of the triangle?