The ratio depends only on the angle
Two right triangles with the same angle have sides in the same proportion, however big they are. That fixed proportion is what sin, cos and tan record.
Class 9 to 12 · 26 games
Trigonometry, explained with pictures
Linking the angles of a right triangle to the lengths of its sides.
In everyday life: Working out the height of a tower from its shadow, or the slope of a ramp.
Three ratios, named by which sides they compare
sin is opposite over hypotenuse, cos is adjacent over hypotenuse, tan is opposite over adjacent. Which side is opposite depends on the angle you picked.
A few angles are worth memorising
30, 45 and 60 degrees come up constantly and have exact values, like sin 30 = 1/2. Knowing them saves you reaching for a calculator.
A worked example
What is sin 30 degrees?
1/2
In a right triangle with a 30 degree angle, the opposite side is always exactly half the hypotenuse.
Words to know
- hypotenuse
- The longest side of a right triangle, opposite the right angle.
- opposite
- The side across from the angle you are working with.
- adjacent
- The side next to your angle that is not the hypotenuse.
In the games
You will match angles to their exact values and read ratios off a labelled triangle.
Skills
- Trigonometric ratios in a right triangle · Class 9
- Exact trigonometric values · Class 10
- Heights and distances · Class 10
- Signs of trigonometric ratios · Class 11
- Inverse trigonometric values · Class 12
By class
Class 9 trigonometry (4) · Class 10 trigonometry (12) · Class 11 trigonometry (6) · Class 12 trigonometry (4)
Practise trigonometry in Tivumo
No download, no account for your child. Classes 3 to 12, more than 1,000 games.