A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is #(17pi)/24# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-03-27T02:34:58

#color(blue)(A_t = (1/2) * a * b * sin C = 7.25 " sq units"#

#a = 8, b = 7, hat A = (5pi)/24, hat B = (17pi)/24#

#"Sum of the three angles of a triangle " = pi^c#

#hat C = pi - hat A - hat B = pi - (5pi)/24 - (17pi)/24 = pi/12#

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

#color(blue)(A_t = (1/2) * 8 * 7 * sin (pi/12) = 7.25 " sq units"#