# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/6, the angle between sides B and C is (pi)/2, and the length of B is 12, what is the area of the triangle?

Jan 21, 2017

The area of the triangle is 41.5692

#### Explanation:

$\frac{\Pi}{2}$ indicates a right angled triangle

Calculating the length of C will allow us to use
$\frac{1}{2} \cdot B a s e \cdot H e i g h t$ to calculate the area

The length of C can be calculated by using
$T a n \left(\frac{\Pi}{6}\right) = 0.5774 = \frac{C}{12}$

Rearranging
$C = 12 \cdot 0.57735 = 6.9282$

Using $\frac{1}{2} \cdot B a s e \cdot H e i g h t$
$\frac{1}{2} \cdot 12 \cdot 6.9288 = 41.56928$