# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 2, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Mar 28, 2016

#### Answer:

Since the given information provided is the case Side-Angle-Side, you can apply the Law of Cosines to solve for the third side.

#### Explanation:

${c}^{2} = {5}^{2} + {2}^{2} - 2 \cdot 5 \cdot 2 \cdot \cos \left(\frac{5 \cdot \pi}{12}\right)$
c = sqrt(5^2+2^2-2*5*2*cos((5*pi)/12)
$c = 4.88$ units long.