TRIGONOMETRY PROBLEMS

Hints on solving trigonometry problems:

• If no diagram is given, draw one yourself.
• Mark the right angles in the diagram.
• Show the sizes of the other angles and the lengths of any lines that are known
• Mark the angles or sides you have to calculate.
• Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.
• Decide whether you will need Pythagoras theorem, sine, cosine or tangent.
• Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.

Example:

Calculate the value of cos θ in the following triangle.

Solution:

Use Pythagoras’ theorem to evaluate the length of PR.

Example:

Calculate the length of the side x, given that tan θ = 0.4

Solution:

Example:

Calculate the length of the side x, given that sin θ = 0.6

Solution:

Using Pythagoras’ theorem:

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