# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 5, respectively, and the angle between A and B is pi/4. What is the length of side C?

Jan 16, 2017

$C = 5 \sqrt{2 - \sqrt{2}}$

#### Explanation:

Using the law of cosines, that states that if $A , B , C$ the lengths of the sides of a triangle, then

C^2 = A^2 + B^2 - 2ABcosθ

where θ is the angle between $A$ and $B$.

C^2 = 25 + 25 - 50cos(π/4)

cos(π/4) = sqrt2/2

${C}^{2} = 50 - 25 \sqrt{2}$

$C = \sqrt{50 - 25 \sqrt{2}} = \sqrt{25 \left(2 - \sqrt{2}\right)} = 5 \sqrt{2 - \sqrt{2}}$