# 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?

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Otis V. Share
Apr 16, 2017

2.95

#### Explanation:

Using the law of cosines which states that the square of a sides length is equal to the sum of the squares of the other 2 sides minus the product of the length of the 2 other sides and the angle between them

${C}^{2} = {A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos \left(c\right)$

$C = \sqrt{4 + 16 - 16 \cos \left(\frac{\pi}{4}\right)} = 2.95$

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