# A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/3, the angle between sides B and C is pi/4, and the length of B is 5, what is the area of the triangle?

Jun 3, 2018

Area A_t color(brown)(= 7.92 sq units

#### Explanation:

Area of triangle ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

Law of Sines $\frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{\sin} C$

$\hat{A} = \frac{\pi}{4} , \hat{C} = \frac{\pi}{3} , \hat{B} = \frac{5 \pi}{12} , b = 5$

$a = \frac{5 \cdot \sin \left(\frac{\pi}{4}\right)}{\sin} \left(\frac{5 \pi}{12}\right) = 3.66$

A_t= (1/2) * 3.66 * 5 * sin (pi/3) color(brown)(= 7.92 sq units