# Question #bf025

Dec 7, 2017

An Obtuse triangle

#### Explanation:

We can solve this by just using the Pythagorean theorem. Acute triangles, obtuse triangles, and right triangles can all be found using this theorem.

We know that the Pythagorean theorem is the proof for a right triangle: ${a}^{2} + {b}^{2} = {c}^{2}$

If we plug in the number 2 for $a$, 3 for $b$, and 7 for $c$ we can determine the type of triangle this is.

For all acute triangles, the following will be true: ${a}^{2} + {b}^{2} > {c}^{2}$
For all obtuse triangles, the following will be true: ${a}^{2} + {b}^{2} < {c}^{2}$
And finally, for all right triangles, the following will be true: ${a}^{2} + {b}^{2} = {c}^{2}$

Since ${2}^{2} + {3}^{2} = 13$ and ${7}^{2} = 49$, we can just plug those numbers into all the proofs.

Acute triangle: $13 > 49$ is false
Obtuse triangle $13 < 49$ is true
And finally, right triangle: $13 = 49$ is also false.

We now know that his triangle is an obtuse triangle.

Hope this helps!
~Chandler Dowd