# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, 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?

Aug 19, 2016

Area of the triangle $= 3$

#### Explanation:

Clearly this is a right-angled triangle
where $b a s e = A = 2 \mathmr{and} h e i g h t = B = 3$ and
angle between $A$ and $B$ =$\pi - \left(\frac{7 \pi}{24} + \frac{5 \pi}{24}\right) = \pi - \left(\frac{\pi}{2}\right) = \frac{\pi}{2}$
Therefore we can write

Area of the triangle $= \frac{1}{2} \times h e i g h t \times b a s e = \frac{1}{2} \times 3 \times 2 = 3$