# How do you classify the triangle given 2 yd, 3 yd, 4 yd?

Jul 14, 2015

This is an obtuse scalene triangle.

#### Explanation:

Let $a = 2$, $b = 3$ and $c = 4$ be the lengths of the sides.

The angle $\gamma$ opposite the side of length $c$ satisfies the law of cosines:

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos \left(\gamma\right)$

So:

$\gamma = \arccos \left(\frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}\right)$

$= \arccos \left(\frac{4 + 9 - 16}{12}\right)$

$= \arccos \left(- \frac{1}{4}\right) > \frac{\pi}{2}$

So the triangle is obtuse.

It is scalene since all the sides are of different lengths.