IGCSE Maths / Further trigonometry

The sine rule: finding a missing side

Edexcel International GCSE Maths (4MA1), chapter 25: Further trigonometry, specification point 4.8c. Free lesson.

Read the revision notes · IGCSE Maths past papers

The sine rule finds a missing side in any triangle, including triangles with no right angle. The key is to pair each side with the angle opposite it.

When to use the sine rule

If a triangle has no right angle, SOH CAH TOA cannot be used. When you know two angles and a side, the sine rule can find another side. It works for any triangle, including one with an obtuse angle. The sine rule is printed on the formula sheet, so you do not need to memorise it. Use two fractions at a time: a/(sin A) = b/(sin B).

Match each side to its opposite angle

In the rule, a and b are sides, while A and B are the angles opposite those sides. An opposite angle is across the triangle from the side, not beside it. Choose the two fractions that match the information you have. Before writing the rule, trace from each known side across the triangle to the angle facing it. Pairing a side with a neighbouring angle is a common error and can lose all the marks.

Find AC in triangle ABC

Here, AC faces angle B, while BC faces angle A. Use those opposite pairs, then rearrange to make AC the subject.

Find AB when the triangle is wide

An obtuse angle does not change the method. AB faces angle C, and AC faces angle B. The same opposite-side pairing works.

Check the size of your answer

Compare the sides and their opposite angles. The longest side must face the biggest angle, so this is a useful check that your pairing and answer make sense. In the first example, AC is longer than BC because angle B is bigger than angle A. In the second example, AB is longer than AC because angle C is bigger than angle B.

More lessons in Further trigonometry