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?

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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"#