New
New
Year 10
Foundation

Checking and securing understanding of tangent ratio problems

I can use the tangent ratio to find the missing side or angle in a right-angled triangle.

New
New
Year 10
Foundation

Checking and securing understanding of tangent ratio problems

I can use the tangent ratio to find the missing side or angle in a right-angled triangle.

Lesson details

Key learning points

  1. The tangent ratio involves the opposite, adjacent and the angle
  2. If you know the length of the opposite and the size of the angle, you can use the tangent ratio
  3. If you know the length of the adjacent and the size of the angle, you can use the tangent ratio
  4. If you know the length of the opposite and adjacent, you can use the tangent ratio

Common misconception

Pupils may confuse the opposite and adjacent sides.

The orientation of the right-angled triangle is not important. Identifying the known angle is what determines which is is the opposite and which is the adjacent.

Keywords

  • Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.

  • Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.

  • Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.

  • Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.

It may be helpful to introduce the tangent formula as a × tan(θ°) = opp, that is to say the length of the side opposite to an angle is equal to the length of the adjacent multiplied by the tangent of that angle, so that both rearrangements of the formula can be shown using a one-step division
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.
Match the names of the sides, relative to the angle $$\theta$$.
An image in a quiz
Correct Answer:a,opposite

opposite

Correct Answer:b,adjacent

adjacent

Correct Answer:c,hypotenuse

hypotenuse

Q2.
The two triangles are similar. What is the length of $$x$$?
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Correct Answer: 1.46 cm, 1.46
Q3.
Triangle ABC and triangle DEF are similar. What is the length of $$x$$?
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Correct Answer: 16 cm, 16, sixteen
Q4.
Work out the value of $$x$$ to 3 significant figures.
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Correct Answer: 4.99, 4.99 cm
Q5.
Work out the value of $$x$$ to 1 decimal place.
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Correct Answer: 8.6, 8.6 cm
Q6.
Work out the length of $$x$$, to 1 decimal place.
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Correct Answer: 12.7 cm, 12.7

6 Questions

Q1.
For a right-angled triangle, the tangent ratio is $$\tan(\theta)=\frac{\text{opp}}{\text{adj}}$$, where $$\theta$$ is the angle in degrees. Which of these are equivalent forms?
$$\tan(\theta)=\frac{\text{adj}}{\text{opp}}$$
Correct answer: $$\text{adj}\times\tan(\theta)=\text{opp}$$
$$\text{adj}=\frac{\tan(\theta)}{\text{opp}}$$
Correct answer: $$\theta=\arctan\left(\frac{\text{opp}}{\text{adj}}\right)$$
Correct answer: $$\text{adj}=\frac{\text{opp}}{\tan(\theta)}$$
Q2.
Work out the length of $$x$$, to 1 decimal place.
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Correct Answer: 11.7 cm, 11.7
Q3.
Work out the length of $$x$$, to 1 decimal place.
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Correct Answer: 10.1 cm, 10.1
Q4.
Using the table of values, what is the value of $$\theta$$?
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0
5
10
Correct answer: 15
20
Q5.
Match the variables to their values.
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Correct Answer:opposite,33

33

Correct Answer:adjacent,48

48

Correct Answer:theta,34.50852299

34.50852299

Q6.
Work out the value of $$\theta$$, to the nearest degree.
An image in a quiz
Correct Answer: 42, forty two, 42 degrees