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)/2, and the length of B is 10, what is the area of the triangle?

$\text{Area"_(triangle"ABC") = 50 "sq.units}$
From the given information we can deduce that the angle between A and C is $\frac{\pi}{4}$
and therefore $\triangle \text{ABC}$ is an isosceles, right-angled triangle with $\left\mid B \right\mid = \left\mid C \right\mid = 10$ and $B \bot C$
Using $B$ as the base and $C$ as the height
$\textcolor{w h i t e}{\text{XXX}} A r e {a}_{\triangle} = \frac{1}{2} \cdot B \cdot C = \frac{1}{2} \cdot 10 \cdot 10 = 50$