A right-angle triangle has sides AB, BC and CA with the right -angle between sides BC and CA. The angle between AB and BC is 24 degrees. The length of AB is 12m. How long is side BC?

Firstly we draw the triangle. From here we can see that the hypotenuse is side AB and the angle we know is between this side and the side we are trying to find the length of. This is when we can use either one of two methods to figure out whether to use sin, cos or tan to work out the length of side BC. The first method is SOHCAHTOA. We have the hypotenuse and the side we are trying to find is the adjacent so we can see we'd use cos. We can also see this because the angle we know is COSy in between the side we are trying to find and the hypotenuse. We can then use cos. cos24=BC/12 which would mean BC=12cos24. Put in a calculator this would give an answer of 10.96m or, to 3s.f. 11.0m.