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.

Thus in the above right-angled triangle, 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 1**

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

**Answer**

By Pythagoras' Theorem,

c^{2 }= 3^{2} + 8^{2}

c^{2} = 9 + 64

c^{2} = 73

c = √73

c =** 8.54 **(to 3 s.f.)

**Example 2**

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.)