# 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 54, what is the area of the triangle?

Mar 15, 2017

The area of the triangle is about $390.69 u n i t {s}^{2}$

#### Explanation:

since $\frac{\pi}{2} = 90$degrees we know this triangle is right
we can find the side of A by saying $\tan \left(\frac{\pi}{12}\right) = \frac{A}{54}$
then rearrange the equation to get $A = 54 \tan \left(\frac{\pi}{12}\right)$
this gives you $A = 14.47$
then you can use the formula for the area of a triangle which is
$\frac{1}{2}$(base)(height)
so the equation would be $\frac{1}{2} \left(54\right) \left(14.47\right)$
This is equal to (390.69)