Using the tangent ratio | Maths | Quizalize & Oak National Academy

Starter quiz

In a right triangle, if the hypotenuse is 25 cm and a second side is 20 cm, what is the perimeter? (Use a calculator to help you.)
- 60 cm ✓
- 66 cm
- 70 cm
In a right triangle, if the hypotenuse is 125 cm and a second side is 100 cm, what is the area? (Use a calculator to help you.)
- $3700 cm^2$
- $3750 cm^2$ ✓
- $3520 cm^2$
What is the value of cos(37ᵒ) to 2 d.p. ?
- 0.80 ✓
- 0.70
- 0.90
Which of these is a correct formula for using the Cosine function?
- $cos(x) = \frac{adj}{hyp}$ ✓
- $cos(x) = \frac{opp}{hyp}$
- $cos(x) = \frac{hyp}{adj}$
- $cos(x) = \frac{adj}{opp}$
Which of these is a correct formula for using the Sine function?
- $sin(x) = \frac{opp}{hyp}$ ✓
- $sin(x) = \frac{opp}{adj}$
- $sin(x) = \frac{adj}{hyp}$
- $sin(x) = \frac{hyp}{opp}$
Which of these is a correct formula for using the Tangent function?
- $tan(x) = \frac{opp}{adj}$ ✓
- $tan(x) = \frac{adj}{opp}$
- $tan(x) = \frac{opp}{hyp}$
- $tan(x) = \frac{hyp}{adj}$

Using triangle ABC, if θ = 38ᵒ and BC = 14 cm, what is the length of the adjacent side AC to 1 d.p. ?
- '17.9' ✓
What value of $y$ will produce the same result for tan( $y$ ) and cos(90ᵒ)?
- 0ᵒ ✓
- 45ᵒ
- 90ᵒ
- 60ᵒ
Using triangle ABC, if θ = 18ᵒ and BC = 10 cm, what is the length of the adjacent side AC to 1 d.p. ?
- '30.8' ✓
What value of $y$ will produce the same result for tan( $y$ ) and cos(0ᵒ)?
- 0ᵒ
- 45ᵒ ✓
- 90ᵒ
- 60ᵒ
Using triangle ABC, if θ =26ᵒ and AC = 10 cm, what is the length of BC to 1 d.p. ?
- '4.9' ✓
Using triangle ABC, if θ =35ᵒ and AC = 10 cm, what is the length of BC to 1 d.p. ?
- '7.0' ✓

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The tangent ratio involves the opposite, adjacent and the angle.
If you know the length of the opposite and the size of the angle, you can use the tangent ratio.
If you know the length of the adjacent and the size of the angle, you can use the tangent ratio.
If you know the length of the opposite and adjacent, you can use the tangent ratio.

Pupils may get the fraction (opposite/adjacent) inverted and this will still return an answer so they may believe they are correct.

Remind pupils to sense check their answers. The larger the angle, the longer the opposite side will be.

Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.
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.