A triangle has sides A, B, and C. If the angle between sides A and B is $(pi)/12$ , the angle between sides B and C is $(7pi)/12$ , and the length of B is 17, what is the area of the triangle?

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Answer 1 · 2018-06-03T01:23:06

Area of triangle $color(green)(A_t = 139.57$ sq units

$hat A = (7pi)/12, hat C = pi/12, hat B = pi/3, b = 17$

Applying Law of Sines, $a / sin A = b / sin B$

$a = (17 * sin ((7pi)/12) )/ sin (pi/3) = 18.96$

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

$A_t = (1/2) * 18.96 * 17 * sin (pi/12) = 139.57$ sq units

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/12(pi)/12, the angle between sides B and C is (7pi)/12(7pi)/12, and the length of B is 17, what is the area of the triangle?