A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/2, the angle between sides B and C is pi/3, and the length of B is 8, what is the area of the triangle?

Jan 1, 2017

The area of the triangle is $55.43 \left(2 \mathrm{dp}\right)$ sq.unit

Explanation:

The angle between sides $A \mathmr{and} B$ is $\angle c = \frac{\pi}{2} = \frac{180}{2} = {90}^{0}$

The angle between sides $B \mathmr{and} C$ is $\angle a = \frac{\pi}{3} = \frac{180}{3} = {60}^{0}$

This is a right triangle with base $B = 8 \therefore \tan a = \frac{A}{B} \mathmr{and} A = B \cdot \tan a \therefore A = 8 \cdot \tan 60 = 8 \cdot \sqrt{3}$

The area of the triangle is ${A}_{t} = \frac{1}{2} \cdot B \cdot A = \frac{1}{2} \cdot 8 \cdot 8 \cdot \sqrt{3} = 32 \cdot \sqrt{3} = 55.43 \left(2 \mathrm{dp}\right)$ sq.unit [Ans]