# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4 and the angle between sides B and C is pi/6. If side B has a length of 2, what is the area of the triangle?

Jul 8, 2017

The area of the triangle is $= 0.74 {u}^{2}$

#### Explanation:

The angle between side $A$ and $C$ is

$= \pi - \left(\frac{1}{4} \pi + \frac{1}{6} \pi\right) = \pi - \frac{5}{12} \pi = \frac{7}{12} \pi$

Applying the sine rule to the triangle

$\frac{A}{\sin} \left(\frac{1}{6} \pi\right) = \frac{B}{\sin} \left(\frac{7}{12} \pi\right) = \frac{2}{\sin} \left(\frac{7}{12} \pi\right) = 2.07$

$A = 2.07 \cdot \sin \left(\frac{1}{2} \pi\right) = 1.04$

The area of the triangle is

$= \frac{1}{2} \cdot A \cdot B \cdot \sin \left(\frac{1}{4} \pi\right) = \frac{1}{2} \cdot 1.04 \cdot 2 \cdot \sin \left(\frac{1}{4} \pi\right) = 0.74 {u}^{2}$