# A triangle has sides of lengths 4, 3, and 5 is it a right triangle?

Jun 12, 2015

Yes, it is.

#### Explanation:

Use the Pythagorean Rule to check;

${5}^{2} = {3}^{3} + {4}^{2}$
25 = 9 + 16 . OK

Jun 12, 2015

Let's see. Let's use the Law of Cosines to check by solving for an angle or two.

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

${5}^{2} = {3}^{2} + {4}^{2} - 2 \left(3\right) \left(4\right) \cdot \cos C$

$0 = - 2 \left(3\right) \left(4\right) \cdot \cos C$

$0 = \cos C$

$C = {90}^{o} , \cancel{{270}^{o}}$

Therefore, with $C = {90}^{o}$ as one of the angles, it is a right triangle.