# A triangle has sides with lengths of 23 meters, 13 meters, and 18 meters. Is it a right triangle?

Jun 13, 2018

No.

#### Explanation:

if it were a right triangle, then ${23}^{2} = {13}^{2} + {18}^{2}$

529 = 169 + 324? No.

By the cos rule, ${23}^{2} = {13}^{2} + {18}^{2} - 2 \cdot 13 \cdot 18 \cdot \cos \theta$

$\theta \ne \frac{\pi}{2}$