New
New
Year 10
Foundation

Applying trigonometric ratios in context

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

New
New
Year 10
Foundation

Applying trigonometric ratios in context

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

Lesson details

Key learning points

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

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.

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.

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.
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).

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6 Questions

Q1.
Which of the trigonometric ratios should you use to calculate $$x$$?
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sine
Correct answer: cosine
tangent
Q2.
Which of the trigonometric ratios should you use to calculate $$x$$?
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Correct answer: sine
cosine
tangent
Q3.
Work out the length of $$x$$, to 1 decimal place.
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Correct Answer: 10.2 cm, 10.2
Q4.
Work out the length of $$x$$, to 1 decimal place.
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Correct Answer: 6.9 cm, 6.9
Q5.
Work out the size of $$x$$, to the nearest degree.
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Correct Answer: 55, 55 degrees
Q6.
Which of these calculations will find the value of $$x$$?
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$$x=8\tan(41^\circ)$$
Correct answer: $$x=\frac{8}{\tan(41^\circ)}$$
Correct answer: $$x=8\tan(49^\circ)$$
$$x=\frac{8}{\tan(49^\circ)}$$

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?
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$$x=\tan\left(\frac{2}{6}\right)$$
$$x=\tan\left(\frac{6}{2}\right)$$
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?
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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?
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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?
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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.
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Correct Answer: 1834 m, 1834
Q6.
Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.
An image in a quiz
Correct Answer: 11.6 m, 11.6