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 #(17pi)/24# and the angle between B and C is # (pi)24#. What is the area of the triangle?

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Answer 1 · 2018-03-26T07:30:40

#color(green)("Area of the given triangle " A_t = 12.37 " sq units"#

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

#hat C = pi - pi/24 - (17pi)/24 = pi/4#

We will use the formila two sides and the included angle to find the area of the given triangle.

#A_t = (1/2) * a * b * sin C = (1/2) * 5 * 7 * sin (pi/4) = 12.37 " sq units"#