# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 7, respectively, and the angle between A and B is (3pi)/8 . What is the length of side C?

Jan 10, 2016

$c = 6.6815$ units.

#### Explanation:

First of all let me denote the sides with small letters $a$, $b$ and $c$
Let me name the angle between side "a" and "b" by $\angle C$.

Note:- the sign $\angle$ is read as "angle".
We are given with $\angle C$

It is given that $a = 1$ and $b = 7$

Using Law of Cosines
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos \angle C$

${c}^{2} = {1}^{2} + {7}^{2} - 2 \cdot 1 \cdot 7 \cos \left(\frac{3 \pi}{8}\right)$

$\implies {c}^{2} = 1 + 49 - 14 \cos \left(\frac{3 \pi}{8}\right)$

$\implies {c}^{2} = 50 - 14 \left(0.38268\right) = 50 - 5.35752 = 44.64248$
$\implies {c}^{2} = 44.64248 \implies c = 6.6815$ units.