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- Year 9
Scaling the right-angled triangle from the unit circle
I can recognise the right-angled triangle within a unit circle and use proportion to scale to similar triangles.
- Year 9
Scaling the right-angled triangle from the unit circle
I can recognise the right-angled triangle within a unit circle and use proportion to scale to similar triangles.
Lesson details
Key learning points
- There are specific ratios within the two key right-angled triangles defined by the unit circle.
- The first right-angled triangle has hypotenuse of length one.
- The opposite and adjacent sides of this triangle have lengths sin(θ) and cos(θ), respectively.
- The second right-angled triangle has an adjacent side length of one.
- The opposite side of this triangle has length tan(θ)
Keywords
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Common misconception
When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate.
Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. However, two decimal places is a reasonable degree of accuracy for reading values from the graphs during this lesson.
To help you plan your year 9 maths lesson on: Scaling the right-angled triangle from the unit circle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Scaling the right-angled triangle from the unit circle, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.In a right triangle, if the hypotenuse is 39 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)
Q2.In a right triangle, if the hypotenuse is 125 cm and a second side is 75 cm, what is the length of the third side? (Use a calculator to help you.)
Q3.In a right triangle, if the hypotenuse is 22.5 cm and a second side is 13.5 cm, what is the perimeter? (Use a calculator to help you.)
Q4.In a right triangle, if the shortest sides are 22.5 cm and 30 cm, what is the length of the hypotenuse? (Use a calculator to help you.)
Q5.Would a right triangle ABC with side AB = 24cm, and hypotenuse AC = 30cm be similar to the one shown in the diagram?

Q6.For this pair of triangles, can you determine whether they are similar without using side lengths?

Assessment exit quiz
6 Questions
Q1.Which letter represents the opposite side to the non-right angle shown in the diagram?

Q2.Which letter represents the opposite side to the non-right angle shown in the diagram?

Q3.Using ABCD, which side would represent the opposite if we were using angle CBD?

Q4.Assuming the two triangles are similar and all measures are in cm, if length AB is 9 what is length BC?

Q5.Assuming the two triangles are similar and all measures are in cm, if length AB is 11 what is length AC?

Q6.Assuming the two triangles are similar and all measures are in cm, if length BC is 3.6 cm what is length AB?
