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      Checking and securing understanding of sine ratio problems

      Lesson details

      Learning outcome

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

      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 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.

      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.

      Teacher tip

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

      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).

      Lesson video

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      Prior knowledge starter quiz

      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 $$x$$?

      An image in a quiz
      Correct Answer: 41, forty one, 41 degrees

      Q5.
      What is the approximate value of $$\sin(60^\circ)$$?

      An image in a quiz
      Correct Answer: 0.87

      Q6.
      What is the approximate value of $$\sin(30^\circ)$$?

      An image in a quiz
      Correct Answer: 0.5

      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.

      An image in a quiz
      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

      To help you plan your 10 maths lesson on: Checking and securing understanding of sine ratio problems, download all teaching resources for free and adapt to suit your pupils' needs...