IGCSE Maths / Introducing trigonometry

The sine ratio

Edexcel International GCSE Maths (4MA1), chapter 16: Introducing trigonometry, specification point 4.8b-f. Free lesson.

Read the revision notes · IGCSE Maths past papers

The sine ratio links an angle in a right-angled triangle to the opposite side and the hypotenuse. Use it to find a missing length, and check that your calculator is set to degrees.

How to label the sides

Name the sides from the angle you are using. The opposite side is the one facing that angle. The hypotenuse faces the right angle and is the longest side. The same side can be opposite in one question and next to the angle in another. Do not label the opposite side from the right angle. Use the other angle in the question.

What the sine ratio measures

For an angle x in a right-angled triangle, sine is the opposite side divided by the hypotenuse. It is a ratio of two lengths, so it has no units. This is the sine ratio: sin x = O/H. The pairing is often remembered as SOH in SOH CAH TOA, but SOH CAH TOA is not on the Edexcel formula sheet. Sine is always opposite over hypotenuse. Because the hypotenuse is the longest side, this ratio is less than 1.

How to find the opposite side

When you know the hypotenuse and the angle, use sine to find the opposite side. Rearrange the ratio by multiplying both sides by the hypotenuse. The side you find must be shorter than the hypotenuse.

How to check your fraction

The hypotenuse belongs underneath the opposite side in the sine ratio. If you put it on top, the ratio can become greater than 1. That cannot be right for an angle in a right-angled triangle, so check the fraction if your answer is too large. A result above 1 is a warning that the fraction may be upside down. A calculator set to radians can give a plausible-looking but incorrect answer.

More lessons in Introducing trigonometry