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Lesson 10 of 13

Year 10
Higher

Applying trigonometric ratios in context

I can apply trigonometric ratios to practical situations including angles of elevation and depression.

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Lesson 10 of 13

New

Year 10
Higher

Applying trigonometric ratios in context

I can apply trigonometric ratios to practical situations including angles of elevation and depression.

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Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

Trigonometric ratios are used in many scenarios
Trigonometric ratios are used to calculate the height of a structure

Keywords

Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.

Common misconception

Using the wrong trigonometric function.

Encourage pupils to draw the right-angled triangle for the scenario if they are unsure so that they can label the sides and be confident about which trigonometric function is needed.

To help you plan your year 10 maths lesson on: Applying trigonometric ratios in context, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils may be interested in further exploring how trigonometry can be useful in the real-world. Consider asking pupils to calculate the heights of various buildings using trigonometry.

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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).

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Prior knowledge starter quiz

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6 Questions

Q1.
Which of the trigonometric ratios should you use to calculate $$x$$?

sine

Correct answer: cosine

tangent

Q2.
Which of the trigonometric ratios should you use to calculate $$x$$?

Correct answer: sine

cosine

tangent

Q3.
Work out the length of $$x$$, to 1 decimal place.

Correct Answer: 10.2 cm, 10.2

Q4.
Work out the length of $$x$$, to 1 decimal place.

Correct Answer: 6.9 cm, 6.9

Q5.
Work out the size of $$x$$, to the nearest degree.

Correct Answer: 55, 55 degrees

Q6.
Which of these calculations will find the value of $$x$$?

$$x=8\tan(41^\circ)$$

Correct answer: $$x=\frac{8}{\tan(41^\circ)}$$

Correct answer: $$x=8\tan(49^\circ)$$

$$x=\frac{8}{\tan(49^\circ)}$$

Assessment exit quiz

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6 Questions

Q1.
A helicopter flies so that it is 6 miles due East and 2 miles due North of where it started. Which calculation finds the angle, $$x$$ to fly direct?

$$x=\tan\left(\frac{2}{6}\right)$$

$$x=\tan\left(\frac{6}{2}\right)$$

Correct answer: $$x=\arctan\left(\frac{2}{6}\right)$$

$$x=\arctan\left(\frac{6}{2}\right)$$

Q2.
A helicopter flies so that it is 2 miles due East and 6 miles due South of where it started. What is the angle, $$x$$, to the nearest degree to fly direct?

Correct Answer: 72

Q3.
A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?

Correct Answer: 5, five, 5 miles

Q4.
A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?

Correct Answer: 3, 3 miles, three

Q5.
A search and rescue helicopter spots a person out at sea. Using the diagram, work out the height of the helicopter above the sea level, to the nearest metre.

Correct Answer: 1834 m, 1834

Q6.
Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.

Correct Answer: 11.6 m, 11.6

Applying trigonometric ratios in context

Applying trigonometric ratios in context

These resources will be removed by end of Summer Term 2025.

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which of the trigonometric ratios should you use to calculate $$x$$?

Q2.Which of the trigonometric ratios should you use to calculate $$x$$?

Q3.Work out the length of $$x$$, to 1 decimal place.

Q4.Work out the length of $$x$$, to 1 decimal place.

Q5.Work out the size of $$x$$, to the nearest degree.

Q6.Which of these calculations will find the value of $$x$$?

Assessment exit quiz

6 Questions

Q1.A helicopter flies so that it is 6 miles due East and 2 miles due North of where it started. Which calculation finds the angle, $$x$$ to fly direct?

Q2.A helicopter flies so that it is 2 miles due East and 6 miles due South of where it started. What is the angle, $$x$$, to the nearest degree to fly direct?

Q3.A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?

Q4.A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?

Q5.A search and rescue helicopter spots a person out at sea. Using the diagram, work out the height of the helicopter above the sea level, to the nearest metre.

Q6.Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.

Q1.
Which of the trigonometric ratios should you use to calculate $$x$$?

Q2.
Which of the trigonometric ratios should you use to calculate $$x$$?

Q3.
Work out the length of $$x$$, to 1 decimal place.

Q4.
Work out the length of $$x$$, to 1 decimal place.

Q5.
Work out the size of $$x$$, to the nearest degree.

Q6.
Which of these calculations will find the value of $$x$$?

Q1.
A helicopter flies so that it is 6 miles due East and 2 miles due North of where it started. Which calculation finds the angle, $$x$$ to fly direct?

Q2.
A helicopter flies so that it is 2 miles due East and 6 miles due South of where it started. What is the angle, $$x$$, to the nearest degree to fly direct?

Q3.
A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?

Q4.
A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?

Q5.
A search and rescue helicopter spots a person out at sea. Using the diagram, work out the height of the helicopter above the sea level, to the nearest metre.

Q6.
Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.