A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 9, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (7pi)/24. What is the area of the triangle?

Feb 15, 2016

9 square units

Explanation:

The sum of the 3 angles in a triangle $= \pi$

the 2 angles here $= \frac{5 \pi}{24} + \frac{7 \pi}{24} = \frac{\pi}{2}$

which means that the 3rd angle $= \pi - \frac{\pi}{2} = \frac{\pi}{2}$

hence this is a right triangle , with C , the hypotenuse.

so area $= \frac{1}{2} \times A \times B = \frac{1}{2} \times 2 \times 9 = \text{ 9 square units}$