# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/4. If side B has a length of 3, what is the area of the triangle?

Dec 17, 2017

$4.5$

#### Explanation:

Note that the sum of all angles in a triangle must be $\pi$ radians (180°).
$\pi - \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$
The remaining angle is $\frac{\pi}{4}$.
Also note that triangle $A B C$ is a right triangle (/_AB=pi/2=90°).

The area of a triangle given the base and height is $\frac{1}{2} b h$.
$\frac{1}{2} \cdot 3 \cdot 3 = 4.5$
Therefore, the area of the triangle is $4.5$.