A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is $(5pi)/24$ and the angle between B and C is $(11pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-27T03:10:31

$color(green)(A_t = 2.6 " sq units"$

$hat A = (11pi)/24, hat B = (5pi)/24, a = 2, b = 3$

$hat C = pi - hat A - hat B = pi - (11pi)/24 - (5pi)/24 = pi/3$

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

$A_t = (1/2) * 2 * 3 * sin (pi/3) = 2.6 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is (5pi)/24(5pi)/24 and the angle between B and C is (11pi)/24 (11pi)/24. What is the area of the triangle?