A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, respectively. The angle between A and C is #(5pi)/8# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-03-26T07:22:03

#color(red)("Area of the triangle " A_t = 3.5 " sq units"#

#a = 2, hat A = (5pi)/24, b = 7, hat B = (5pi)/8#

#hat C = pi - (5pi)/24 - (5pi) / 8 = pi/6#

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/1wTkLqIGQSW4SInCvt8F_area%20of%20triangle.png)

We know now two sides and the included angle.

We will use the formula #A_t = (1/2) a b sin C#

#A_t = (1/2) * 2 * 7 * sin (pi/6) = 3.5 " sq units"#