Sine, Cosine and Tangent Ratios (9)

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223)

Apply trigonometry to solve right-angled triangle problems (ACMMG224)

LO: To investigate the Sine, Cosine and Tangent ratios and use trigonometry to solve right-angled triangle problems.


  • the properties of right-angled triangles.

  • that the hypotenuse is the longest side of a right-angled triangle.

  • 3 sides of a right-angled triangle can be labelled as adjacent, opposite and hypotenuse.


  • That there is a link between the sine, cosine and tangent ratios in right-angled triangles


  • I can use the sine, cosine and tangent ratios to solve related right-angled triangle problems.

Properties of Right-Angled Triangles

One thing to keep in mind when labelling the corresponding sides is that the labels are relative to the given angle (usually we call it theta).

“Opposite” is the opposite to the angle.
“Adjacent” is next to the angle.
“Hypotenuse” is the long side of the right-angled triangle and is always opposite of the right angle.

There are 3 ratios used in trigonometry to help identify the length of the sides of a right-angled triangle.

sin angle = opposite side / hypotenuse

cos angle = adjacent side / hypotenuse

tan angle = opposite side / adjacent side


Teaching Ideas

Trigonometry Videos

BBC Trigonometry
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