Pythagoras' theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written algebraically: a^{2}+b^{2}=c^{2}
where c represents the length of the hypotenuse and a and b are the two shorter sides.
In some cases, where the sides of the right-angled triangle form a Pythagorean triad, the exact length of the hypotenuse is an integer value. But for most cases we will end up with an irrational number , that is, a surd.
If we are asked to give an exact answer, or to answer as a surd, we can stop our working out when we arrive at a line of working such as c=\sqrt{11}, as this can not be simplified without losing some accuracy when it is rounded.
Find the length of the unknown side c in the triangle below. Give the answer as a surd.
To find the length of the hypotenuse we can use Pythagoras' theorem: