Question

Suppose that a triangle has side lengths of 10, 11, and 17. Is the triangle as acute, obtuse, or right? How do you know? Explain.

Answer 1

This is an Obtuse Triangle

Explanation:

Start by calculating the squares of each side. We know that if sum of squares of two smaller sides equal the largest side, it is a right triangle (Pythagoras theorem).

`10^2 = 100`
`11^2 = 121`
`17^2 = 289`

We note that `100+121=221 < 289`, this is a property of an obtuse triangle.

Following is a general rule for a triangle with three sides, `a,b,c`, where `a\leb\lec`.

Right Triangle `=> a^2+b^2 = c^2`
Acute Triangle `=> a^2+b^2 > c^2`
Obtuse Triangle `=> a^2+b^2 < c^2`

You can verify it by trying an equilateral triangle (which is an acute triangle), `a = 1, b= 1, c=1`