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Year 9

Using the sine ratio

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

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Year 9

Using the sine ratio

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

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Share activities with pupils
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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.

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 function - 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.

Common misconception

The sine formula is only used to find the length of a side opposite an angle.

Whilst the sine formula can be used to find the length of a side opposite an angle, a rearrangement of the formula also allows us to find the length of the hypotenuse given the opposite side. The arcsine function allows us to find the angle, itself.


To help you plan your year 9 maths lesson on: Using the sine ratio, download all teaching resources for free and adapt to suit your pupils' needs...

It may be helpful to introduce the sine formula as h × sin(θ°) = opp, that is to say the length of the side opposite an angle is equal to the length to the hypotenuse multiplied by the sine of that angle, so that both rearrangements of the formula can be shown using a one-step division.
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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).

Lesson video

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Starter quiz

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6 Questions

Q1.
In a right triangle, if the hypotenuse is 15 cm and a second side is 9 cm, what is the perimeter? (Use a calculator to help you.)
Correct answer: 36 cm
32 cm
41 cm
Q2.
What is the value of θ for cos(θ) = 0
Correct answer: 90ᵒ
45ᵒ
30ᵒ
0ᵒ
Q3.
In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)
Correct answer: $$150 cm^2 $$
$$140 cm^2 $$
$$300 cm^2 $$
Q4.
Which of these is a rearrangement of $$tan(θ)=\frac{opp}{adj}$$
$$tan(θ)=\frac{adj}{opp}$$
$$opp=\frac{tan(θ)}{adj}$$
Correct answer: $$adj=\frac{opp}{tan(θ)}$$
Q5.
In a right triangle, if you are provided with θ and the hypotenuse, which function would you use to find the opposite side?
Correct answer: Sine
Cosine
Tangent
Q6.
In a right triangle, if θ = 35ᵒ and the opposite side is 7 cm, what is the length of the hypotenuse to the nearest whole number?
Correct answer: 12 cm
9 cm
10cm

Exit quiz

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6 Questions

Q1.
Using triangle ABC, if θ = 35ᵒ and BC = 5 cm, what is the length of the hypotenuse AB to 1 d.p. ?
An image in a quiz
Correct Answer: 8.7, 8.7 cm
Q2.
What value of $$x$$ will produce the same result for cos($$x$$) and sin(30ᵒ)?
30ᵒ
Correct answer: 60ᵒ
90ᵒ
Q3.
Using triangle ABC, if θ = 40ᵒ and BC = 4.8 cm, what is the length of the hypotenuse AB to 1 d.p. ?
An image in a quiz
Correct Answer: 7.5, 7.5cm
Q4.
What value of $$y$$ will produce the same result for sin($$y$$) and cos(26ᵒ)?
36ᵒ
46ᵒ
Correct answer: 64ᵒ
54ᵒ
Q5.
Using triangle ABC, if θ = 50ᵒ and AB = 12 cm, what is the length of side BC to 1 d.p. ?
An image in a quiz
Correct Answer: 9.2, 9.2cm
Q6.
Using triangle ABC, if θ = 45ᵒ and AB = 18 cm, what is the length of side BC to 1 d.p. ?
An image in a quiz
Correct Answer: 12.7, 12.7cm