# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Jan 26, 2017

The area of the triangle is $15.16 \left(2 \mathrm{dp}\right) s q . u n i t$

#### Explanation:

The angle between sides A and C is $\angle b = \frac{5 \pi}{24} = 5 \cdot \frac{180}{24} = {37.5}^{0}$

The angle between sides B and C is $\angle a = \frac{\pi}{8} = \frac{180}{8} = {22.5}^{0}$

The angle between sides A and B is $\angle c = 180 - \left(37.5 + 22.5\right) = {120}^{0}$

So we have sides A=7 ; B=5  and their included angle $\angle c = {120}^{0}$

The area of the triangle is ${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} = \frac{7 \cdot 5 \cdot \sin 120}{2} = 15.16 \left(2 \mathrm{dp}\right) s q . u n i t$ [Ans]