A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2018-03-27T02:21:46

#A_t = (1/2) * a * b * sin C = 5.18 " sq units"#

#hat B = (13pi)/24, hat A = (3pi) / 8, a = 5, b = 8#

To find the area of the triangle.

#hat C = pi - hat A - hat B = pi - (3pi) / 8 - (13pi) / 24 = pi/12#

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

#A_t = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"#