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.

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.

345θ
Small triangle
6810θ
Twice as big, same angle

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.

435θ
Opposite, adjacent and hypotenuse

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.

30°
30 degrees
45°
45 degrees
60°
60 degrees

A worked example

What is sin 30 degrees?

30°
At 30 degrees the height is 1/2

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

Practise trigonometry in Tivumo

No download, no account for your child. Classes 3 to 12, more than 1,000 games.