Sine and cosine ratios | Maths | Quizalize & Oak National Academy

Starter quiz

In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the length of the third side? (Use a calculator to help you.)

20 cm ✓

22 cm

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

Yes, because their three angles correspond. ✓

No because you only know two angles.

No, because you always need a side and two angles.
What is cos(60ᵒ)?

0.5 ✓

0.1

0

1
In a right triangle, if the shortest sides are 40 cm and 96 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

100 cm

104 cm ✓

108 cm
Which of the following statements is true for these triangles?

The triangles are similar. ✓

The triangles are not similar.

It is not possible to know whether the triangles are similar or not.
Would a triangle ABC with sides AB = 32cm, BC = 24cm, AC = 40cm be similar to the one shown in the diagram?

Yes ✓

No

Exit quiz

Which side would we label as 'adjacent' to the non-right angle shown?

A

B ✓

C
In a right triangle, if you are provided with θ and the adjacent side, which function would you use to find the hypotenuse?

Sine

Cosine ✓

Tangent
In a right triangle, if θ = 35ᵒ and the opposite side is 4 cm, what is the length of the hypotenuse to the nearest whole number?

'7 cm' ✓
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 ✓
In a right triangle, if θ = 40ᵒ and the adjacent side is 9 cm, what is the length of the hypotenuse to the nearest whole number?

'12 cm' ✓
In a right triangle, if θ = 50ᵒ and the hypotenuse is 12 cm, what is the length of the adjacent side to the nearest whole number?

'8 cm' ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

When the hypotenuse has a length of one, the opposite side has length sin⁡(θ)
When the hypotenuse has a length of one, the adjacent side has length cos⁡(θ)
Any right-angled triangle is a scaled version of this triangle.

Common misconception

sin(60°) is double sin(30°).

The values of the sine or cosine of an angle do not scale linearly. We can see from the unit circle that an angle of 30° meets the circle at a height of 0.5 units, whilst an angle of 60° meets the circle at a height of approximately 0.87 units.

Keywords

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right 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.
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.