# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 6, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

Apr 16, 2018

$2.719 u n i t s$ to 3 decimal places

#### Explanation:

$\frac{\pi}{8} \times \frac{180}{\pi} = {22.5}^{\circ} = {22}^{\circ} 30 '$

Use the cosine rule:-

$\therefore {c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

$\therefore {c}^{2} = {7}^{2} + {6}^{2} - 2 a b \cos {22}^{\circ} 30 '$

$\therefore {c}^{2} = 49 + 36 - \left(2 \cdot 7 \cdot 6 \cdot 0.0923879532\right)$

$\therefore {c}^{2} = 49 + 36 - \left(77.60588076\right)$

$\therefore {c}^{2} = 7.39411924$

$\therefore \sqrt{{c}^{2}} = \sqrt{7.39411924}$

$\therefore c = 2.719212982$

$\therefore c = 2.719 u n i t s$ to 3 decimal places