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Year 9

Problem solving with trigonometry

I can use my knowledge of trigonometry to solve problems.

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New
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Year 9

Problem solving with trigonometry

I can use my knowledge of trigonometry to solve problems.

Download all resources
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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Sometimes there can be more than one valid approach to a problem.
  2. You should consider all the skills you have.
  3. Consider multiple approaches and take time to evaluate each.
  4. Keep the goal in mind throughout, remember what you are trying to find out.

Keywords

  • Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

Common misconception

Pupils may struggle to identify a right-angled triangle in the problem.

Encourage pupils to sketch the question out and add any known right angles or perpendicular lines, as this may lead to a right-angled triangle.


To help you plan your year 9 maths lesson on: Problem solving with trigonometry, download all teaching resources for free and adapt to suit your pupils' needs...

Provide multiple copies of a regular octagon and ask the pupils to discuss and evaluate different methods to find the area of it. This could then be extended to a regular decagon and see if the pupils prefer one method to another.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
In a right triangle, if the shortest sides are 48 cm and 20 cm, what is the length of the hypotenuse?
Correct answer: 52 cm
50 cm
54 cm
Q2.
Which of the following statements is true for these triangles?
An image in a quiz
Correct answer: The triangles are similar.
The triangles are not similar.
It is not possible to know whether the triangles are similar or not.
Q3.
In a right triangle, if the hypotenuse is 45 cm and a second side is 36 cm, what is the length of the third side? (Use a calculator to help you.)
28 cm
Correct answer: 27 cm
26 cm
Q4.
In a right triangle, if the hypotenuse is 15 cm and a second side is 12 cm, what is the perimeter? (Use a calculator to help you.)
34 cm
Correct answer: 36 cm
32 cm
Q5.
For this pair of triangles, can you determine whether they are similar without using side lengths?
An image in a quiz
Correct answer: Yes, because their three angles correspond.
No because you only know two angles.
No, because you always need a side and two angles.
Q6.
Could an equilateral triangle be similar to the triangle below?
An image in a quiz
Yes
Correct answer: No

Exit quiz

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6 Questions

Q1.
Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 30ᵒ. What is the height of the triangle to 2 d.p. ?
Correct Answer: 1.15 cm, 1.15
Q2.
Isosceles triangle ABC has base 9 cm and ∠ABC = ∠BCD = 42ᵒ. What is the height of the triangle?
Correct Answer: 4.05 cm, 4.05
Q3.
What is the area of an equilateral triangle of side 4 cm to 2 d.p. ?
Correct Answer: 3.46, 3.46 cm^2
Q4.
Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 20ᵒ. What is the area of the triangle to 2 d.p. ?
Correct Answer: 1.46, 1.46 cm ^2
Q5.
Isosceles triangle ABC has base 5 cm and ∠ABC = ∠BCD = 24ᵒ. What is the perimeter of the triangle to 2 d.p. ?
Correct Answer: 9.57, 9.57 cm
Q6.
A yacht sails 50 km due East and then 60 km due South. If the yacht is still facing South, how many degrees clockwise (2d.p.) should it turn to be facing directly towards its starting point.
Correct Answer: 140.19, 140.19ᵒ