New
New
Year 9
Choosing the right trigonometric ratio
I can choose the appropriate trigonometric ratio to use to solve problems in right-angled triangles.
New
New
Year 9
Choosing the right trigonometric ratio
I can choose the appropriate trigonometric ratio to use to solve problems in right-angled triangles.
Lesson details
Key learning points
- When selecting the appropriate trigonometric ratio, consider what information you have been given.
- When selecting the appropriate trigonometric ratio, consider what you are trying to find.
- If you do not have enough information, consider what you need and how you will get it.
- Trigonometric ratios involve two lengths and an angle.
Common misconception
Pupils may believe the horizontal edge of the triangle is always the adjacent.
Emphasise that the labelling of the triangle is based around the focus angle and use right-angled triangles with various orientations.
Keywords
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Encourage pupils to identify the given information before attempting the question. This will help them to consider which of the trigonometric ratios they can use and what they might need to answer the question in hand.
Teacher tip
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
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6 Questions
Q1.
Which of the following statements is true for these triangles?
Correct answer: The triangles are similar.
The triangles are similar.
The triangles are not similar.
It is not possible to know whether the triangles are similar or not.
Q2.
What is the value of θ for tan(θ) = 1
Correct answer: 45ᵒ
45ᵒ
90ᵒ
30ᵒ
0ᵒ
Q3.
What is cos(0ᵒ)?
Correct answer: 1
1
0
undefined
0.5
Q4.
What is sin(30ᵒ)?
1
0
undefined
Correct answer: 0.5
0.5
Q5.
For sin(xᵒ) = y, which of these statements is true?
Correct answer: cos(90 - xᵒ) = y
cos(90 - xᵒ) = y
tan(90 - xᵒ) = y
cos(yᵒ) = x
tan(yᵒ) = x
Q6.
In a right triangle, if the hypotenuse is 50 cm and a second side is 30 cm, what is the area? (Use a calculator to help you.)
$$700 cm^2 $$
Correct answer: $$600 cm^2 $$
$$600 cm^2 $$
$$900 cm^2 $$
Exit quiz
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6 Questions
Q1.
Tick which approaches could be used to find $$x$$ without finding further sides or angles given the information provided in the diagram.
$$a^2+b^2=c^2$$
There is not enough information to solve this problem.
$$sin(θ)=\frac{opp}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
Correct answer: $$tan(θ)=\frac{opp}{adj}$$
$$tan(θ)=\frac{opp}{adj}$$
Q2.
Tick which approaches could be used to find $$x$$ given the information provided in the diagram.
Correct answer: $$a^2+b^2=c^2$$
$$a^2+b^2=c^2$$
There is not enough information to solve this problem.
Correct answer: $$sin(θ)=\frac{opp}{hyp}$$
$$sin(θ)=\frac{opp}{hyp}$$
Correct answer: $$cos(θ)=\frac{adj}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
Correct answer: $$tan(θ)=\frac{opp}{adj}$$
$$tan(θ)=\frac{opp}{adj}$$
Q3.
Tick which approaches could be used to find $$x$$ without finding more angles and given the information provided in the diagram.
Correct answer: $$a^2+b^2=c^2$$
$$a^2+b^2=c^2$$
There is not enough information to solve this problem.
$$sin(θ)=\frac{opp}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
$$tan(θ)=\frac{opp}{adj}$$
Q4.
Tick which approaches could be used to find $$x$$ given the information provided in the diagram.
$$a^2+b^2=c^2$$
Correct answer: Basic properties of triangles
Basic properties of triangles
$$sin(θ)=\frac{opp}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
$$tan(θ)=\frac{opp}{adj}$$
Q5.
Tick which approaches could be used to find the angle without finding the remaining side, given the information provided in the diagram.
$$a^2+b^2=c^2$$
Correct answer: Basic properties of triangles
Basic properties of triangles
$$sin(θ)=\frac{opp}{hyp}$$
Correct answer: $$cos(θ)=\frac{adj}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
$$tan(θ)=\frac{opp}{adj}$$
Q6.
Tick which approach is the simplest to find $$x$$ given the information provided in the diagram.
$$a^2+b^2=c^2$$
Correct answer: Basic properties of triangles
Basic properties of triangles
$$sin(θ)=\frac{opp}{hyp}$$
$$cos(θ)=\frac{adj}{hyp}$$
$$tan(θ)=\frac{opp}{adj}$$