A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 6, respectively. The angle between A and C is $(11pi)/24$ and the angle between B and C is $(11pi)/24$ . What is the area of the triangle?

Question

1811 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-27T07:13:59

$color(green)(Delta " " A_t = (1/2) a b sin C = 5.44 " sq units"$

$hat A = (11pi)/24, hat B = (11pi)/24, a = 7, b = 6$

$hat C = pi - (11pi)/24 - (11pi)/24 = pi/12$

![https://www.onlinemathlearning.com/http://area-triangle.html](https://useruploads.socratic.org/PWUT3gSRQRWDQWi3GEvR_area%20of%20triangle.png)

$color(blue)("Using two sides and included angle formula"$

$color(green)(Delta " " A_t = (1/2) a b sin C = (1/2) * 7 * 6 * sin (pi/12) = 5.44 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 6, respectively. The angle between A and C is (11pi)/24(11pi)/24 and the angle between B and C is (11pi)/24 (11pi)/24. What is the area of the triangle?