how to find the hypotenuse

Unit 3 Section 2 : Calculating the Hypotenuse

If we know the two shorter lengths in a right-angled triangle, we can use Pythagoras' Theorem to find the hypotenuse.

Example Question

Look at the triangle below.

We want to find the length of the hypotenuse (h).

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 h� is equal to 5� + 12�.

So the length of the hypotenuse (h) can be worked out as follows:

h�	=	5� + 12�	(work out the squares of the two shorter sides)
h�	=	25 + 144	(add the squares of the two shorter sides together)
h�	=	169	(square root both sides to find the value of h)
h	=	13

We can now see that the length of the hypotenuse (h) is 13m.

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 d� is equal to (1.5)� + (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.

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the

button to find out whether you have answered correctly. If you are right then

will appear and you should move on to the next question. If

appears then your answer is wrong. Click on

to clear your original answer and have another go. If you can't work out the right answer then click on

to see the answer.

You have now completed Unit 3 Section 2

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Produced by A.J. Reynolds February 2003 >