## Right Angle Reasoning

#### Problem

In a right angle triangle the side opposite the right angle is called the hypotenuse.

Explain why the hypotenuse must be the longest side.

#### Solution

It should be clear that as the size of the angle increases, length of the opposite side also increase.

We know that the sum of angles in any (planar) triangle is 180 degrees. So if one of the angles is a right angle then the other two angles must add to 90 degress between them and neither of them can equal or exceed 90 degrees.

Hence the biggest angle in a right angle triangle must be the right angle and it follows that the longest side is opposite the right angle; that is, the hypotenuse is the longest side.

Problem ID: 252 (12 Dec 2005) Difficulty: 1 Star