Classify a triangle with sides 6, 8, 9 by its angles

Step by step

The question

Question: find what kind of triangle has sides 6, 8, 9, by its angles.

1 Find the longest side

The longest side is 9.

We call it c.

The biggest angle is across from it.

2 Compare the squares

Square the two short sides: 6² is 36, 8² is 64.

Together: 100.

Square the longest side: 9² is 81.

100 is more than 81: c is too short for a right angle.

The angle across from c is narrower than 90°, and it is the biggest angle.

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 acute.

Let's look back.

First: find the longest side.

Then: compare the squares.

Last: name it.