# A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 4, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (13pi)/24. What is the area of the triangle?

Jun 13, 2017

The area of the triangle is $= \sqrt{2} = 1.41 {u}^{2}$

#### Explanation:

The angle between $A$ and $C$ is

$= \pi - \left(\frac{5}{24} \pi + \frac{13}{24} \pi\right)$

$= \pi - \frac{18}{24} \pi$

$= \frac{6}{24} \pi = \frac{1}{4} \pi$

The area of the triangle $\Delta A B C$ is

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

$= \frac{1}{2} \cdot 1 \cdot 4 \cdot \frac{\sqrt{2}}{2}$

$= \sqrt{2}$

$= 1.41$