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

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Answer 1 · 2015-06-12T17:49:21

Yes, it is.

Use the Pythagorean Rule to check;

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

Answer 2 · 2015-06-12T17:49:44

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

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

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

$0 = - 2 (3) (4) \cdot cos C$ $0 = - 2(3)(4)*cosC$

$0 = cos C$ $0 = cosC$

$C = 90^o, cancel(270^o)$

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