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

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

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

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

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/7uFhgQhSyu3C8wYujzg0_area%20of%20triangle.png)

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

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

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