# 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 2, what is the area of the triangle?

Jan 16, 2016

0.53589838486
I do not have my scientific calculator with me, so my answer could be wrong. However, these are the steps to solve them

#### Explanation:

The angle between A and C:
-The sum of an angle is $\Pi$

$\Pi - \frac{\Pi}{2} - \frac{\Pi}{12} = 5 \frac{\Pi}{12}$

Find either side of A/C using the sine rule:
What is sine rule> http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/furthertrigonometryhirev1.shtml

For A;
$\frac{A}{\sin} \left(\frac{\Pi}{12}\right) = \frac{2}{\sin} \left(5 \frac{\Pi}{12}\right)$
$A = \frac{2 \cdot \sin \left(\frac{\Pi}{12}\right)}{\sin} \left(5 \frac{\Pi}{12}\right)$
$A = 0.53589838486$

. Using the $\frac{1}{2} \left(A\right) \left(B\right) \sin C$ What is the formula for area of triangle (http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/furthertrigonometryhirev3.shtml) to find the area.

$\frac{1}{2} \left(0.53589838486\right) \left(2\right) \sin \left(\frac{\Pi}{2}\right) = 0.53589838486$