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

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Answer 1 · 2018-04-10T02:46:04

$:.color(brown)(A_t = (1/2) * 4.39 * 12 * sin ((2pi)/3) = 22.81 " sq units"$

$hat A = pi/12, hat C = (2pi)/3, hat B = pi - pi/12 - (2pi)/3 = pi/4, b = 12$

$color(purple)(a / sin A = b / sin B = c / sin C)$

$:. a = (b * sin A) / sin B = (12 * sin (pi/12)) / sin (pi/4) = 4.39$

$color(indigo)("Area of " Delta " " A_t = (1/2) * a * b * sin C$

$:.color(brown)(A_t = (1/2) * 4.39 * 12 * sin ((2pi)/3) = 22.81 " sq units"$

A triangle has sides A,B, and C. If the angle between sides A and B is (2pi)/32π3(2pi)/3, the angle between sides B and C is pi/12π12pi/12, and the length of B is 12, what is the area of the triangle?