Pythagoras: Finding missing sides
We can use Pythagoras' Theorem to find a missing hypotenuse (longest side) on a right-angled triangle. We know that if we square the two short sides on the triangle and add them together, we get the square on the hypotenuse. From this, we can square-root to find the length of the hypotenuse.
We can leave the answer in surd form or work it out on a calculator. In GCSE problems, you will often need to round your answer to a given number of decimal places or significant figures.
To solve problems using Pythagoras' Theorem algebraically, you will need to be familiar with the basics of solving equations and rearranging formulae.
If your algebra skills aren't quite there yet, you can use SASH to help you remember what to do:
(to find the) Hypotenuse.
Scroll down for revision notes on this method, or watch an example on YouTube.
We can also use Pythagoras' Theorem to find a missing short side on a right-angled triangle. We know that the difference between the square on the hypotenuse and the square on the short side we know will be equal to the square on the missing short side. From this, we can square-root to find the length of the missing short side.
You can use SSSS to help you remember what to do:
(to find a) Short Side.
You can watch an example problem on finding a short side on my YouTube channel.