# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2. If side C has a length of 25  and the angle between sides B and C is pi/12, what is the length of side A?

$\frac{C}{\sin} C = \frac{A}{\sin} A$
Given side $C = 25$ , $\angle C = \left(\frac{\pi}{2}\right)$ & $\angle A = \left(\frac{\pi}{12}\right)$
$\therefore \frac{25}{\sin} \left(\frac{\pi}{2}\right) = \frac{A}{\sin} \left(\frac{\pi}{12}\right)$
$A = \frac{25 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\pi / 2\right)$
$A = \frac{25 \cdot \sin \left(\frac{\pi}{12}\right)}{1} = 25 \cdot 0.2588 =$ 6.4705