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Year 10
Foundation

Checking and securing understanding of sine ratio problems

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

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New
New
Year 10
Foundation

Checking and securing understanding of sine ratio problems

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

Download all resources
Share activities with pupils

Lesson details

Key learning points

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

Common misconception

Incorrectly rearranging the sine formula.

A ratio table can be helpful to see the relationship between the sides and therefore how to rearrange.

Keywords

  • Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

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

  • 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.

Some pupils may benefit from labelling the sides of the triangle first before attempting to use the sine formula.
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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Starter quiz

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6 Questions

Q1.
Two shapes are if the only difference between them is their size. Their side lengths are in the same proportions.
congruent
Correct answer: similar
matching
Q2.
Triangle ABC and triangle DEF are similar. What is the length of side $$x$$?
An image in a quiz
Correct Answer: 116 cm, 116
Q3.
Triangle ABC and triangle DEF are similar. What is the length of side $$x$$?
An image in a quiz
Correct Answer: 26 cm, 26
Q4.
The two triangles are similar. What is the size of the angle marked $$x$$?
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Correct Answer: 41, forty one, 41 degrees
Q5.
What is the approximate value of $$\sin(60^\circ)$$?
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Correct Answer: 0.87
Q6.
What is the approximate value of $$\sin(30^\circ)$$?
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Correct Answer: 0.5

Exit quiz

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6 Questions

Q1.
Work out the length of $$x$$, given that these two triangles are similar.
An image in a quiz
Correct Answer: 3.1 cm, 3.1
Q2.
Work out the length of $$x$$, given that these two triangles are similar.
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Correct Answer: 6 cm, 6, six
Q3.
For a right-angled triangle, the sine ratio is $$\sin(\theta)=\frac{\text{opp}}{\text{hyp}}$$, where $$\theta$$ is the angle in degrees. Which of these are equivalent forms?
$$\sin(\theta)=\frac{\text{hyp}}{\text{opp}}$$
Correct answer: $$\text{hyp}\times\sin(\theta)=\text{opp}$$
$$\text{hyp}=\frac{\sin(\theta)}{\text{opp}}$$
Correct answer: $$\theta=\arcsin\left(\frac{\text{opp}}{\text{hyp}}\right)$$
Correct answer: $$\text{hyp}=\frac{\text{opp}}{\sin(\theta)}$$
Q4.
Which of the following equations are correct when finding the angle $$n^\circ$$ in the equation: $$\sin(n^\circ)=0.38$$?
$$n=\frac{0.38}{\sin()}$$
$$n=\sin(0.38)$$
Correct answer: $$n=\arcsin(0.38)$$
Correct answer: $$n=\sin^{-1}(0.38)$$
Q5.
Which of these is correct for this triangle?
An image in a quiz
$$\sin(x)=\frac{3}{5}$$
$$\sin(x)=\frac{5}{3}$$
Correct answer: $$\sin(x)=\frac{4}{5}$$
$$\sin(x)=\frac{5}{4}$$
$$\sin(x)=\frac{4}{3}$$
Q6.
Calculate the length of $$x$$ to 2 decimal places.
An image in a quiz
Correct Answer: 7.06 cm, 7.06