Question

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?

Answer 1

`4.5`

Explanation:

Note that the sum of all angles in a triangle must be `pi` radians (`180°`).
`pi-pi/2-pi/4=pi/4`
The remaining angle is `pi/4`.
Also note that triangle `ABC` is a right triangle (`/_AB=pi/2=90°`).

The area of a triangle given the base and height is `1/2bh`.
`1/2*3*3=4.5`
Therefore, the area of the triangle is `4.5`.