# 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/4, and the length of B is 4, what is the area of the triangle?

Feb 20, 2016

area = 8 square units

#### Explanation:

Since the angle between A and B is $\frac{\pi}{2} \text{ then this is a right triangle with side C , the hypotenuse}$

Further , since the angle between B and C is $\frac{\pi}{4}$

Then the angle between A and C must be $\frac{\pi}{4}$

Making this a right isosceles triangle. Hence B = 4 then A = 4

and Area = $\frac{1}{2} \times B \times A = \frac{1}{2} \times 4 \times 4 = 8 \text{ square units}$