Trigonometric ratios in right-angled triangles
Grow and shrink a right-angled triangle with a 35° angle and see that the sides change but their ratio doesn't. Then name the opposite, adjacent and hypotenuse for each angle, and find a side and an angle from a table of values, without a calculator.
- UK: Year 9
- France: grade 8
- Germany: grade 9
- Iran: grade 10
- Afghanistan: grade 9
- Syria: grade 9
- Palestine: grade 8
- Ukraine: grade 8
- Russia: grade 8
Guide
For Year 9 (KS3: trigonometric ratios in similar triangles), Afghan Grade 9 and Iran Grade 10. The coloured dots can be dragged; the readouts under the figure update live.
In triangle ABC the right angle is at B, and AC, opposite the right angle, is the hypotenuse. For angle A, BC is the opposite side and AB the adjacent side. For angle C they swap; the hypotenuse is always AC.
sin A = BC/AC, cos A = AB/AC and tan A = BC/AB (SOH CAH TOA). These ratios depend only on the angle, not on the size of the triangle, because all right-angled triangles with a 35° angle are similar.
sin 35° is a number (about 0.57), not "sin times 35". The other way round, if you know the ratio you can find the angle in the table: that is written sin⁻¹, meaning "the angle whose sine is this number", not 1 divided by sin.