A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is $(7pi)/24$ and the angle between B and C is $(5pi)/8$ . What is the area of the triangle?

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Answer 1 · 2018-03-26T07:01:41

$color(indigo)("Area of the triangle "A_t ~~ 10.87 " sq units"$

$a = 12, b = 7, hatA = (5pi)/8, hat B = (7pi)/24$

$hat C = pi - hat A - hat B = pi - (5pi)/8 - (7pi)/24 = pi/12$

Having known, two sides and the included angle (SAS), area of the triangle is given by the formula

$color(indigo)(A_t = (1/2) a b sin C = (1/2) * 12 * 7 * sin (pi/12) ~~ 10.87 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is (7pi)/24(7pi)/24 and the angle between B and C is (5pi)/8 (5pi)/8. What is the area of the triangle?