# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 4, respectively, and the angle between A and B is (pi)/2 . What is the length of side C?

Jun 18, 2018

color(violet)(c = sqrt (5^2 + 4^2) ~~ 6.4 " units"

#### Explanation:

$\therefore {c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

$\text{Given : } a = 5 , b = 4 , \hat{C} = \frac{\pi}{2}$

${c}^{2} = {5}^{2} + {4}^{2} + \left(2 \cdot 5 \cdot 4 \cdot \cos \left(\frac{\pi}{2}\right)\right) = {5}^{2} + {4}^{2}$

as $\cos \left(\frac{\pi}{2}\right) = 0$

color(violet)(c = sqrt (5^2 + 4^2) ~~ 6.4 " units"