# 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 9, what is the area of the triangle?

Aug 12, 2016

$= 10.85$

#### Explanation:

Clearly this is a right-angled triangle where $b a s e = B = 9$ and angle between $A$ and $C$ =$\pi - \left(\frac{\pi}{2} + \frac{\pi}{12}\right) = \pi - \left(\frac{7 \pi}{12}\right) = \frac{5 \pi}{12}$
Therefore we can write
$\frac{B}{A} = \tan \left(\frac{5 \pi}{12}\right)$
or
$\frac{9}{A} = 3.73$
or
$A = \frac{9}{3.73}$
or
$A = 2.41$ (Pl.note $A$ is the $h e i g h t$)
Area of the triangle $= \frac{1}{2} \times h e i g h t \times b a s e = \frac{1}{2} \times 2.41 \times 9 = 10.85$