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"#