# 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/12. If side B has a length of 12, what is the area of the triangle?

Dec 30, 2015

$A r e a = S = 19.292$

#### Explanation:

If the angle between A and B is $\frac{\pi}{2}$ then the triangle is a right one and its area is:
$S = \frac{A \cdot B}{2}$

Since the angle between B and C is known and the length of B also is known, we can find A in this way:
$\tan \left(\frac{\pi}{12}\right) = \left(\text{opposed cathetus")/("adjacent cathetus}\right)$
So $\tan \left(\frac{\pi}{12}\right) = \frac{A}{B}$ => $A = B \cdot \tan \left(\frac{\pi}{12}\right)$

Finally,
$S = \frac{{B}^{2} \cdot \tan \left(\frac{\pi}{12}\right)}{2}$
$S = \frac{{12}^{2} \cdot 0.267949}{2} = 19.292$