A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (11pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-03-27T02:38:31

#color(green)(A_t = (1/2) * a * b * sin C = 7.071 " sq units"#

#a = 4, hat A = (11pi)/24, b = 5, hat B = (7pi)/24#

#hat C = pi - hat A - hat B = pi - (11pi)/24 - (7pi)/24 = pi/4#

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

#color(green)(A_t = (1/2) * 4 * 5 * sin (pi/4) = 7.071 " sq units"#