Classify a triangle with sides 5, 12, 13 by its angles

Step by step

The question

Question: find what kind of triangle has sides 5, 12, 13, by its angles.

1 Find the longest side

The longest side is 13.

We call it c.

The biggest angle is across from it.

2 Compare the squares

Square the two short sides: 5² is 25, 12² is 144.

Together: 169.

Square the longest side: 13² is 169.

169 and 169 are the same.

That is Pythagoras: the angle across from c is 90°.

Only the biggest angle decides the name.

Careful!

The longest side is across from the biggest angle.

So c is always the longest side.

3 Name it

So the triangle is right.

Let's look back.

First: find the longest side.

Then: compare the squares.

Last: name it.