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"#