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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
You have the opposite and hypotenuse side lengths so
use the sine ratio: sin x = 5/7
x = sinˉ¹(5/7) = 46°
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
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.