A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is $(pi)/8$ and the angle between B and C is $(7pi)/12$ . What is the area of the triangle?

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Answer 1 · 2018-03-26T07:07:34

$color(brown)("Area of the triangle " A_t = (1/2) a * b * sin C = 71.4 " sq units"$

$a = 12, hat A = (7pi)/12, b = 15, hat B = pi/8$

To find the area of the triangle.

Third angle $hat C = pi - (7pi)/12 - pi / 8 = (7pi) / 24$

Now we know, side a, side b and included ange C.

$A_t = (1/2) a * b * sin C = (1/2) * 12 * 15 * sin ((7pi) / 24) = 71.4 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is (pi)/8(pi)/8 and the angle between B and C is (7pi)/12 (7pi)/12. What is the area of the triangle?