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

Starter quiz

In a right triangle, if the hypotenuse is 15 cm and a second side is 9 cm, what is the perimeter? (Use a calculator to help you.)

36 cm ✓

32 cm

41 cm
What is the value of θ for cos(θ) = 0

90ᵒ ✓

45ᵒ

30ᵒ

0ᵒ
In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)

$150 cm^2$ ✓

$140 cm^2$

$300 cm^2$
Which of these is a rearrangement of $tan(θ)=\frac{opp}{adj}$

$tan(θ)=\frac{adj}{opp}$

$opp=\frac{tan(θ)}{adj}$

$adj=\frac{opp}{tan(θ)}$ ✓
In a right triangle, if you are provided with θ and the hypotenuse, which function would you use to find the opposite side?

Sine ✓

Cosine

Tangent
In a right triangle, if θ = 35ᵒ and the opposite side is 7 cm, what is the length of the hypotenuse to the nearest whole number?

12 cm ✓

9 cm

10cm

Exit quiz

Using triangle ABC, if θ = 35ᵒ and BC = 5 cm, what is the length of the hypotenuse AB to 1 d.p. ?

'8.7' ✓
What value of $x$ will produce the same result for cos( $x$ ) and sin(30ᵒ)?

30ᵒ

60ᵒ ✓

90ᵒ
Using triangle ABC, if θ = 40ᵒ and BC = 4.8 cm, what is the length of the hypotenuse AB to 1 d.p. ?

'7.5' ✓
What value of $y$ will produce the same result for sin( $y$ ) and cos(26ᵒ)?

36ᵒ

46ᵒ

64ᵒ ✓

54ᵒ
Using triangle ABC, if θ = 50ᵒ and AB = 12 cm, what is the length of side BC to 1 d.p. ?

'9.2' ✓
Using triangle ABC, if θ = 45ᵒ and AB = 18 cm, what is the length of side BC to 1 d.p. ?

'12.7' ✓

Worksheet

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Lesson Details

Key learning points

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

Common misconception

The sine formula is only used to find the length of a side opposite an angle.

Whilst the sine formula can be used to find the length of a side opposite an angle, a rearrangement of the formula also allows us to find the length of the hypotenuse given the opposite side. The arcsine function allows us to find the angle, itself.

Keywords

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Trigonometric function - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.