# A triangle has sides A, B, and C. The angle between sides A and B is pi/3 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?

Sep 2, 2016

C = 1.79 and A = 0.53

#### Explanation:

Let the other sides of the Triangle be A and C.

then, $A \cdot \cos \left(\frac{\pi}{3}\right) + C \cdot \cos \left(\frac{\pi}{12}\right) = B = 2$

and $A \cdot \sin \left(\frac{\pi}{3}\right) = C \cdot \sin \left(\frac{\pi}{12}\right)$

ie $\frac{A}{2} + C \cdot 0.9659 = 2$

and $A \frac{\sqrt{3}}{2} = C \cdot 0.2588$

solve to get the answer as C = 1.79 and A = 0.53