# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is (pi)/4 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Feb 17, 2018

Doesn’t qualify to form a triangle

#### Explanation:

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

Given $a = 4 , b = 7 , \hat{B} = \frac{\pi}{4} , \hat{A} = \frac{\pi}{8}$

$\hat{C} = \pi - \frac{\pi}{8} - \frac{\pi}{4} = \frac{5 \pi}{8}$

$\frac{a}{\sin} A = \frac{4}{\sin} \left(\frac{\pi}{8}\right) = 10.4525$

$\frac{b}{\sin} B = \frac{7}{\sin} \left(\frac{\pi}{4}\right) = 9.8995$

$\frac{a}{\sin} A \ne \frac{b}{\sin} B$

Hence doesn’t qualify to form a triangle