# 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 45, what is the area of the triangle?

Feb 14, 2016

271.299

#### Explanation:

the angle between A and B = $\frac{\Pi}{2}$ so the triangle is a right-angled triangle.

In a right-angled triangle, the tan of an angle = $\frac{O p p o s i t e}{A \mathrm{dj} a c e n t}$

Substituting in the known values
$T a n \left(\frac{\Pi}{2}\right) = 3.7320508 = \frac{45}{A \mathrm{dj} a c e n t}$

Rearranging and simplifying
$A \mathrm{dj} a c e n t = 12.057713$

The area of a triangle = $\frac{1}{2} \cdot b a s e \cdot h e i g h t$

Substituting in the values
$\frac{1}{2} \cdot 45 \cdot 12.057713 = 271.299$