# A triangle has sides A, B, and C. Sides A and B are of lengths 6 and 5, respectively, and the angle between A and B is (pi)/2 . What is the length of side C?

side $c = \sqrt{61} = 7.81025$ units

#### Explanation:

Given data side $a = 6$ and side $b = 5$, angle $C = \frac{\pi}{2}$
By the Law of Cosines

$c = \sqrt{{a}^{2} + {b}^{2} - 2 \cdot a \cdot b \cdot \cos C}$
$c = \sqrt{{6}^{2} + {5}^{2} - 2 \cdot 6 \cdot 5 \cdot \cos \left(\frac{\pi}{2}\right)}$
$c = \sqrt{36 + 25 - 0}$
$c = \sqrt{61}$
$c = 7.81025$

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