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There are three trigonometry ratios that relate angles and sides in any right-angled triangle.

sin x = opposite/hypotenuse cos x = adjacent/hypotenuse tan x = opposite/adjacent

Example:

You have the opposite and hypotenuse side lengths so

use the sine ratio: sin x = 5/7

x = sinˉ¹(5/7) = 46°

Example:

You have the adjacent and need to find the opposite side length so

use the tan ratio: tan 55° = x/28

28 x tan 55° = x = 40

GCSE formula bookmark (Etsy website)

Further secondary maths resources are available by clicking the links below.

Consolidate knowledge of trigonometry ratios with these activity worksheets. You will find included: a trigonometry codebreaker worksheet and two word problem worksheets.

Introduction to topic or refresher worksheet looking at using the trigonometric ratios to calculate missing angles. (Printable pdf)

A set of trigonometry ratio worksheets asking to calculate the missing lengths before matching to the answers. You will find included: a sine ratio worksheet, a cosine ratio worksheet, a tangent ratio worksheet and a mixed ratio worksheet.

Trigonometry Activities