If we know the two shorter lengths in a rightangled triangle, we can use Pythagoras' Theorem to find the hypotenuse.
Pythagoras' Theorem tells us:
The square of the hypotenuse is equal to the sum of the squares of the two shorter sides.
In this case, this means that h² is equal to 5² + 12².
So the length of the hypotenuse (h) can be worked out as follows:
We can now see that the length of the hypotenuse (h) is 13m.
h²
=
5² + 12²
(work out the squares of the two shorter sides)
h²
=
25 + 144
(add the squares of the two shorter sides together)
h²
=
169
(square root both sides to find the value of h)
h
=
13
Practice Questions
(a) Look at the triangle below.
We want to find the length of the hypotenuse (d).
Pythagoras' Theorem tells us:
The square of the hypotenuse is equal to the sum of the squares of the two shorter sides.
In this case, this means that d² is equal to (1.5)² + (2)².
Work out the length of the hypotenuse (d) using the method above, then click
to see if you are correct.
(b) Look at the triangle below.
We want to find the length of the hypotenuse (s).
Work out the length of the hypotenuse (s) to 1 decimal place, then check your answer below.
