Pythagoras' Theorem states that:

**In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.**

In the right-angled triangle below a^{2} + b^{2} = c^{2}

Remember that the triangle must be right-angled and that the hypotenuse is always the longest side and the one opposite the right angle.

**Example**

Use Pythagoras' Theorem to calculate the length of the side, a, in the following right-angled triangle. Give your answer to 3 significant figures.

**Answer**

By Pythagoras' Theorem:

a^{2} + 5^{2} = 9^{2}

a^{2} + 25 = 81

a^{2} = 81 - 25 =56

a = √56

c =** 7.48 **(to 3 s.f.)

Let's have a go at some questions.