A right-angled triangle has one angle size 60 degrees, and hypotenuse of length 32cm. Calculate the length of the side opposite the 60 degree angle, to 3sf.

Firstly, we want to draw out the triangle. No matter what the question asks, just draw out all the information you're given so that you can see what the question is asking. We've been given a right angle triangle with a known angle and a known side. For right-angled triangles, there are two sets of formulas you need to know - Pythagoras and Trigonometry. Pythagoras is helpful when you have two of the sides and want to work out the third. Trigonometry is helpful when the angles are involved as well.Here, we only have one side along with an angle so we need to use trigonometry. We'll use the mnemonic SOH CAH TOA to work out which formula we need: here, we have the O and the H, so we'll use sin60=O/H, or sin60=x/32. We can rearrange this to make x=32(sin60), which you can punch into your calculator to work out 27.7128... We'll take the first 3 figures to make the opposite side 27.7cm.