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).

#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#