Choosing the right trigonometric ratio | Maths | Quizalize & Oak National Academy

Starter quiz

Which of the following statements is true for these triangles?

The triangles are similar. ✓

The triangles are not similar.

It is not possible to know whether the triangles are similar or not.
What is the value of θ for tan(θ) = 1

45ᵒ ✓

90ᵒ

30ᵒ

0ᵒ
What is cos(0ᵒ)?

1 ✓

0

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0.5
What is sin(30ᵒ)?

1

0

undefined

0.5 ✓
For sin(xᵒ) = y, which of these statements is true?

cos(90 - xᵒ) = y ✓

tan(90 - xᵒ) = y

cos(yᵒ) = x

tan(yᵒ) = x
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.)

$700 cm^2$

$600 cm^2$ ✓

$900 cm^2$

Exit quiz

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.

$sin(θ)=\frac{opp}{hyp}$

$cos(θ)=\frac{adj}{hyp}$

$tan(θ)=\frac{opp}{adj}$ ✓
Tick which approaches could be used to find $x$ given the information provided in the diagram.

$a^2+b^2=c^2$ ✓

There is not enough information to solve this problem.

$sin(θ)=\frac{opp}{hyp}$ ✓

$cos(θ)=\frac{adj}{hyp}$

$tan(θ)=\frac{opp}{adj}$ ✓
Tick which approaches could be used to find $x$ without finding more angles and given the information provided in the diagram.

$a^2+b^2=c^2$ ✓

There is not enough information to solve this problem.

$sin(θ)=\frac{opp}{hyp}$

$cos(θ)=\frac{adj}{hyp}$

$tan(θ)=\frac{opp}{adj}$
Tick which approaches could be used to find $x$ given the information provided in the diagram.

$a^2+b^2=c^2$

Basic properties of triangles ✓

$sin(θ)=\frac{opp}{hyp}$

$cos(θ)=\frac{adj}{hyp}$

$tan(θ)=\frac{opp}{adj}$
Tick which approaches could be used to find the angle without finding the remaining side, given the information provided in the diagram.

$a^2+b^2=c^2$

Basic properties of triangles ✓

$sin(θ)=\frac{opp}{hyp}$

$cos(θ)=\frac{adj}{hyp}$ ✓

$tan(θ)=\frac{opp}{adj}$
Tick which approach is the simplest to find $x$ given the information provided in the diagram.

$a^2+b^2=c^2$

Basic properties of triangles ✓

$sin(θ)=\frac{opp}{hyp}$

$cos(θ)=\frac{adj}{hyp}$

$tan(θ)=\frac{opp}{adj}$

Worksheet

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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.