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.

1 Answer
Dec 8, 2017

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).

102=100
112=121
172=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 abc.

Right Triangle a2+b2=c2
Acute Triangle a2+b2>c2
Obtuse Triangle a2+b2<c2

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