# A triangle has sides A, B, and C. The angle between sides A and B is pi/6 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?

Mar 3, 2016

≈ 0.366 square units

#### Explanation:

I recommend you make a sketch.

Area can be calculated using either of the following formulae.

area $= \frac{1}{2} A B \sin \left(\frac{\pi}{6}\right) \text{ or } \frac{1}{2} B C \sin \left(\frac{\pi}{12}\right)$

depending on which is used A or C will be required.

choose side A : Require use of $\textcolor{b l u e}{\text{ sine rule }}$

The angle between A and C will also be required before progressing.

angle between A and C $= \pi - \left(\frac{\pi}{6} + \frac{\pi}{12}\right) = \frac{3 \pi}{4}$

sine rule : $\frac{A}{\sin \left(\frac{\pi}{12}\right)} = \frac{B}{\sin \left(\frac{3 \pi}{4}\right)}$

rArr A = (2sin(pi/12))/(sin(3pi)/4) ≈ 0.732

$\Rightarrow \text{ area " = 1/2ABsin(pi/6) ≈ 0.366 " square units }$