Tangent ratio | Maths | Quizalize & Oak National Academy

Starter quiz

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.)
- 75 cm ✓
- 80 cm
- 70 cm
What is the value of θ for sin(θ) = tan(θ) ?
- 0ᵒ ✓
- 45ᵒ
- 90ᵒ
What is the value of θ for tan(θ) = 1
- 45ᵒ ✓
- 90ᵒ
- 30ᵒ
- 0ᵒ
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.)
- $187.5 cm^2$ ✓
- $197.5 cm^2$
- $207.5 cm^2$
What is the value of θ for sin(θ) = 1
- 90ᵒ ✓
- 45ᵒ
- 50ᵒ
- 30ᵒ
What is the value of θ for sin(θ) = cos(θ) ?
- 45ᵒ ✓
- 90ᵒ
- 30ᵒ
- 0ᵒ

Exit quiz

Match the estimated values with the trigonometric functions below.
- sin(23°)
  
  ⇔
  
  0.39 ✓
- cos(39°)
  
  ⇔
  
  0.777 ✓
- tan(22°)
  
  ⇔
  
  0.404 ✓
- tan(45°)
  
  ⇔
  
  1 ✓
For which value of θ is tan (θ) undefined?
- '90' ✓
In a right triangle, if you are provided with θ and the opposite side, which function would you use to find the adjacent side?
- Sine
- Cosine
- Tangent ✓
Which of these is a rearrangement of $tan(θ)=\frac{opp}{adj}$
- $tan(θ)=\frac{adj}{opp}$
- $opp=\frac{tan(θ)}{adj}$
- $adj=\frac{opp}{tan(θ)}$ ✓
Which of these is not an rearrangement of $tan(θ)=\frac{opp}{adj}$
- $adj=\frac{opp}{tan(θ)}$
- $tan(θ)\times adj=opp$
- $tan(θ)=\frac{adj}{opp}$ ✓
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?
- 0.545 cm (3 d.p)
- 0.649 cm (3 d.p) ✓
- 1 cm

Worksheet

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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.

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.

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.