# A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/4, the angle between sides B and C is pi/4, and the length of B is 9, what is the area of the triangle?

Apr 3, 2016

The Area of the triangle $= 20.25$ units

#### Explanation:

Opposite angle of side C is $\angle C = \frac{\pi}{4} = \frac{180}{4} = {45}^{0}$
Opposite angle of side A is $\angle A = \frac{\pi}{4} = \frac{180}{4} = {45}^{0} \therefore \angle B = 180 - \left(45 + 45\right) = {90}^{0}$ Using sine law $\frac{A}{\sin} A = \frac{B}{\sin} B \mathmr{and} A = 9 \cdot \left(\sin \frac{45}{\sin} 90\right) = \frac{9}{\sqrt{2}}$Since it is a right angled isocelles triangle, Side $B = \frac{9}{\sqrt{2}}$ The Area of the triangle $= \frac{1}{2} \cdot C \cdot A$ or Area$= \frac{1}{2} \cdot \frac{9}{\sqrt{2}} \cdot \frac{9}{\sqrt{2}} = \frac{81}{4} = 20.25$ Units[Ans]