Myths about teaching can hold you back
- Year 9
- Year 9
Tangent ratio
I can derive the tangent ratio from the sides of a right-angled triangle.
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Lesson details
Key learning points
- When the adjacent has a length of one, the opposite side has a length of tan(θ).
- You can apply a scale factor to this triangle to find the scaled length of the opposite side.
- There is a multiplicative link between two similar right-angled triangles.
- There is a multiplicative link within each right-angled triangle.
Keywords
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.
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common misconception
tan(60°) is double tan(30°).
The values of tan of an angle do not scale linearly. From the unit circle, we see that an angle of 30° meets a tangent to the circle at a height of approx. 0.58 units, whilst an angle of 60° meets the same tangent at a height of approx. 1.73 units.
To help you plan your year 9 maths lesson on: Tangent ratio, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Tangent ratio, 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.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 3 maths lessons from the Trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Prior knowledge starter quiz
6 Questions
Q1.In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the perimeter? (Use a calculator to help you.)
Q2.What is the value of θ for sin(θ) = tan(θ) ?
Q3.What is the value of θ for tan(θ) = 1
Q4.In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the area? (Use a calculator to help you.)
Q5.What is the value of θ for sin(θ) = 1
Q6.What is the value of θ for sin(θ) = cos(θ) ?
Assessment exit quiz
6 Questions
Q1.Match the estimated values with the trigonometric functions below.
sin(23°) -
0.39
cos(39°) -
0.777
tan(22°) -
0.404
tan(45°) -
1
Q2.For which value of θ is tan (θ) undefined?
Q3.In a right triangle, if you are provided with θ and the opposite side, which function would you use to find the adjacent side?
Q4.Which of these is a rearrangement of $$tan(θ)=\frac{opp}{adj}$$
Q5.Which of these is not an rearrangement of $$tan(θ)=\frac{opp}{adj}$$
Q6.For a right triangle ABC, if angle CBA = 33ᵒ, and the adjacent side to that angle is 1 cm, what is the length of the side opposite angle CBA?