This theorem is only used for **right-angled triangles**.

In a right-angled triangle, there is always **one 90º angle** and the **sum of the other two angles is always to 90º**.

The side opposite the 90º is always the longest side. The longest side is called the **hypotenuse**.

In the triangle above, ∠CAB = 90º

We know sum of all angles of a triangle = 180º

∠CAB + ∠ACB + ∠CBA = 180º

Since ∠CAB = 90º,

90 + ∠ACB + ∠CBA = 180º

∠ACB + ∠CBA = 90º

Since ∠CAB = 90º, the side opposite ∠CAB (i.e. CB) is the hypotenuse.

According to Pythagoras’ Theorem,

**Hypotenuse² = (2nd side)² + (3rd side)²**

Using the above triangle as an example, we can form the equation:

CB² = AB² + AC²

If we have the value of AB and AC and we want to find the value of CB, we do the following:

CB = √(AB² + AC²)

If we have the value of CB and AC and we want to find the value of AB, we rearrange to get the following:

CB² – AC² = AB²

AB = √(CB² – AC²)

If we have the value of CB and AB and we want to find the value of AC, we rearrange to get the following:

CB² – AB² = AC²

AC = √(CB² – AB²)