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

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Answer 1 · 2015-07-14T20:27:00

This is an obtuse scalene triangle.

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:

$c^2=a^2+b^2-2ab cos(gamma)$

So:

$gamma = arccos((a^2+b^2-c^2)/(2ab))$

$=arccos((4+9-16) / 12)$

$=arccos(-1/4) > pi/2$

So the triangle is obtuse.

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