Classify a triangle with sides 6, 7, 10 by its angles

Step by step

The question

Question: find what kind of triangle has sides 6, 7, 10, by its angles.

1 Find the longest side

The longest side is 10.

We call it c.

The biggest angle is across from it.

2 Compare the squares

Square the two short sides: 6² is 36, 7² is 49.

Together: 85.

Square the longest side: 10² is 100.

85 is less than 100: c is too long for a right angle.

The angle across from c is wider than 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 obtuse.

Let's look back.

First: find the longest side.

Then: compare the squares.

Last: name it.