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# Similar triangles and ratios – sin, cos and tan

In the right-angled triangle below, the green side is called the *hypotenuse*.

For the reference angle given in blue, the blue side is called the *opposite* side.

The red side is called the adjacent side.

Pick an angle and stick with it.

Work out the value of \(\dfrac{\color{Blue}{opposite}}{\color{Green}{hypotenuse}}\) as you change the size of the triangle. What do you notice?

Work out the value of \(\dfrac{\color{Red}{adjacent}}{\color{Green}{hypotenuse}}\) as you change the size of the triangle. What do you notice?

Work out the value of \(\dfrac{\color{Blue}{opposite}}{\color{Red}{adjacent}}\) as you change the size of the triangle. What do you notice?

# Trigonometric ratios – sin, cos and tan

**Teachers**: log in to access the following:

- Worksheet G20b Trigonometric ratios
- Handout (condensed format for reduced printing)
- G20b Skills drill worksheet (15 questions on one side of A4; answers included)
- Card sort G20b Trigonometric ratios – choosing whether to use sin, cos or tan
- G20b Trigonometric ratios Random Question Generator – suitable for use on an interactive whiteboard. Answers available.

**Teachers**: log in to access these.

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- G20c – Inverse trigonometric functions
- Trigonometry assorted problems – requiring knowledge of G20a, G20b, G20c, G22a, G22b, and G23a
- A12c – Graphs of trigonometric functions