You may also like

problem icon

Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

problem icon

Power Quady

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

problem icon


Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

Calculating with Cosines

Age 14 to 18 Challenge Level:


If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...


If I tell you two sides of a right-angled triangle, you can easily work out the third using Pythagoras' theorem. But what if the angle between the two sides is not a right angle? Is there a way to work out the length of the third side?

Some students tried to work out a formula to work out the length of the third side when we know two sides and the angle between them.


Below, you can see the start of their methods. Can you finish each method to produce a formula?

Student 1:

Student 2:

Student 3:


Does each method lead to an equivalent formula?

Does each method work for both acute- and obtuse-angled triangles?