A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $(17pi)/24$ and the angle between B and C is $(5pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-27T02:34:58

$color(blue)(A_t = (1/2) * a * b * sin C = 7.25 " sq units"$

$a = 8, b = 7, hat A = (5pi)/24, hat B = (17pi)/24$

$"Sum of the three angles of a triangle " = pi^c$

$hat C = pi - hat A - hat B = pi - (5pi)/24 - (17pi)/24 = pi/12$

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

$color(blue)(A_t = (1/2) * 8 * 7 * sin (pi/12) = 7.25 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is (17pi)/24(17pi)/24 and the angle between B and C is (5pi)/24 (5pi)/24. What is the area of the triangle?