# Pythagoras Theorem Questions

Welcome to our Pythagoras' Theorem Questions area.

Here you will find help, support and questions to help you master Pythagoras' Theorem and apply it.

## Pythagoras' Theorem Questions

### Pythagoras' theorem

#### $a^2 + b^2 = c^2$

where a,b and c are the sides of a right triangle.
Side c is the hypotenuse (longest side).

### Pythagoras' Theorem - in more detail

#### Example 1) Find the length of the missing side.

In this example, we need to find the hypotenuse (longest side of a right triangle).

So using pythagoras, the sum of the two smaller squares is equal to the square of the hypotenuse.

This gives us $4^2 + 6^2 = ?^2$

So $?^2 = 16 + 36 = 52$

This gives us $? = \sqrt {52} = 7.21 \; cm \; to \; 2 \; decimal \; places$

#### Example 2) Find the length of the missing side.

In this example, we need to find the length of the base of the triangle, given the other two sides.

So using pythagoras, the sum of the two smaller squares is equal to the square of the hypotenuse.

This gives us $?^2 + 5^2 = 8^2$

So $?^2 = 8^2 - 5^2 = 64 - 25 = 39$

This gives us $? = \sqrt {39} = 6.25 \; cm \; to \; 2 \; decimal \; places$

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