# A triangle has sides A, B, and C. Sides A and B are of lengths 14 and 9, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Jul 23, 2017

#### Answer:

The length of side $C$ is $19.32 \left(2 \mathrm{dp}\right)$ unit.

#### Explanation:

Sides are $A = 14 , B = 9$ and their included angle

$\angle c = \frac{5 \pi}{8} = \frac{5 \cdot 180}{8} = {112.5}^{0}$

Applying cosine law we can find side C as

$C = \sqrt{{A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos c}$ or

$C = \sqrt{{14}^{2} + {9}^{2} - 2 \cdot 14 \cdot 9 \cdot \cos 112.5} \approx 19.32 \left(2 \mathrm{dp}\right)$ unit

The length of side $C$ is $19.32 \left(2 \mathrm{dp}\right)$ unit. [Ans]