# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 4, respectively, and the angle between A and B is pi/4. What is the length of side C?

Mar 25, 2018

color(indigo)("Length of side " c = sqrt (4 + 16 - (16/sqrt2)) ~~ 8.69 " Units"

#### Explanation:

$G i v e n : a = 2 , b = 4 , \hat{C} = \frac{\pi}{4}$

To find $\text{Length of side c}$

Applying Law of Cosines,

$c = \sqrt{{a}^{2} + {b}^{2} - \left(2 a b \cos C\right)}$

$c = \sqrt{{2}^{2} + {4}^{2} - \left(2 \cdot 2 \cdot 4 \cdot \cos \left(\frac{\pi}{4}\right)\right)}$

color(indigo)(c = sqrt (4 + 16 - (16/sqrt2)) ~~ 8.69