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

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Answer 1 · 2018-03-27T11:42:40

#color(purple)(A_t = (1/2) a b sin C = 8.75 " sq units"#

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

To find the area of the triangle #A_t#

#hat C = pi - (5pi)/24 - (5pi)/8 = pi/6#

#color(purple)(A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin (pi/6) = 8.75#