Question

Determine if the values 3, 5, and 7 represent the side lengths of a right triangle, an obtuse triangle, or an acute triangle. Justify your answer.

Answer 1

It's an acute triangle.

Explanation:

In a triangle ABC with longest side C:

If
`c^2>a^2+b^2` then ABC is acute

If
`c^2=a^2+b^2` then ABC is right

If If
`c^2<a^2+b^2` then ABC is obtuse

In this case A=3, B=5 and C=7. Let's see:

`7^2 ? 3^2+5^2`

`49 ?  9+25`

`49 >  34`

As 49 is bigger than 34, then ABC is acute.