A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/6, the angle between sides B and C is pi/6, and the length of B is 7, what is the area of the triangle?

Jun 21, 2017

The area of the triangle is $= 3.03 {u}^{2}$

Explanation:

The triangle is an isoceles triangle.

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

$= \pi - \left(\frac{1}{6} \pi + \frac{1}{6} \pi\right)$

$= \frac{2}{3} \pi$

The height of the triangle is

$h = \frac{3}{2} \tan \left(\frac{1}{6} \pi\right)$

The area of the triangle is

$A = \frac{1}{2} \cdot b \cdot h$

$= \frac{1}{2} \cdot 7 \cdot \frac{3}{2} \tan \left(\frac{1}{6} \pi\right)$

$= \frac{21}{4} \tan \left(\frac{1}{6} \pi\right)$

$= 3.03$