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 #(pi)/4# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2018-03-27T03:57:35

#color(blue)(Delta " " A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin ((5pi)/8) = 16.17#

#a = 5, b = 7, hat A = pi/8, hat B = pi/4#

To find the area of the triangle.

#hat C = pi - pi / 8 - pi/4 = (5pi)/8#

#Delta " " A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin ((5pi)/8) = 16.17 " sq units"#