Cosine rule

Sample Cosine rule questions

A few of the 35 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 13 marksGrade 6-7
   the tower, the bridge and the pier are three locations. The distance from the tower to the bridge is 14.2 m, the distance from the tower to the pier is 11.6 m, and the distance from the bridge to the pier is 14.1 m. Work out the angle at the tower (the angle between the routes to the bridge and to the pier). Give your answer correct to 1 decimal place.
   Show the worked solution

   The angle at the tower is enclosed by the two sides going TO the tower (lengths 14.2 and 11.6), so the side OPPOSITE this angle is the the bridge-to-the pier distance, 14.1 M1

   $\cos(\text{angle}) = \dfrac{14.2^2 + 11.6^2 - 14.1^2}{2 \times 14.2 \times 11.6} = 0.417$

What are the common mistakes in Cosine rule?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Mishandles a sign when substituting into or rearranging the cosine rule

  Rearranged the cosine rule incorrectly - the correct rearrangement is $\cos(\text{angle}) = \dfrac{b^2+c^2-a^2}{2bc}$

Quick answers about Cosine rule

How many Cosine rule practice questions are there?

There are 35 self-marking GCSE and IGCSE Maths questions on Cosine rule, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Cosine rule?

No. You can start practising Cosine rule straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.