Trigonometry: finding a side with sine

The Maths Habit

A kite flies on a 30 m string.
How could you find how high it is?

Rearrange each formula.

density = massvolumeMake mass the subject.mass = density × volume
density = massvolumeMake volume the subject.volume = massdensity
p = qrMake q the subject.q = pr
p = qrMake r the subject.r = qp

Trigonometry
The maths of how the side lengths and angles of a triangle are linked.
Hypotenuse
The longest side. It is opposite the right angle.
Opposite
The side opposite the angle θ.
Adjacent
The side next to the angle θ that is not the hypotenuse.

Which side is the hypotenuse, the opposite and the adjacent?

Question 1
  • Hypotenuser
  • Oppositep
  • Adjacentq
Question 2
  • Hypotenuseu
  • Oppositet
  • Adjacents
Question 3
  • Hypotenusek
  • Oppositen
  • Adjacentm
Question 4
  • Hypotenusee
  • Oppositeg
  • Adjacentf

sin θ = OH

Casio fx-83GT X calculator
fx-83GT X
Casio fx-83GT CW calculator
fx-83GT CW

Find the sin button.
Check your calculator is in degrees.

  1. sin 41°

    0.656

  2. sin 8°

    0.139

  3. sin 63.5°

    0.895

Rearrange the formula.

sin θ = OH

  1. Make O the subject.

    O = H × sin θ

  2. Make H the subject.

    H = Osin θ

Finding a side with sine

  1. Labelthe opposite O and the hypotenuse H from the angle.
  2. Writesin θ = O ÷ H with the numbers in.
  3. RearrangeMake the unknown the subject of the formula.
  4. CalculateUse your calculator. Round to the accuracy asked for.
Label O and H from the angle.
sin 53° = x9.2
x = 9.2 × sin 53°
x = 7.3 cm
sin 38° = x12
x = 12 × sin 38°
x = 7.4 cm
Label O and H from the angle.
sin 53° = x9.2
x = 9.2 × sin 53°
x = 7.3 cm
sin 52° = x9.5
x = 9.5 × sin 52°
x = 7.5 cm
Label O and H from the angle.
sin 40° = 9x
x = 9 ÷ sin 40°
x = 14.0 cm
sin 28° = 5x
x = 5 ÷ sin 28°
x = 10.7 cm
Label O and H from the angle.
sin 40° = 9x
x = 9 ÷ sin 40°
x = 14.0 cm
sin 61° = 13x
x = 13 ÷ sin 61°
x = 14.9 cm
Label O and H from the angle.
sin 40° = 9x
x = 9 ÷ sin 40°
x = 14.0 cm
sin 50° = x12
x = 12 × sin 50°
x = 9.2 cm
Label O and H from the angle.
sin 40° = 9x
x = 9 ÷ sin 40°
x = 14.0 cm
sin 34° = 5.3x
x = 5.3 ÷ sin 34°
x = 9.5 m
Label O and H from the angle.
sin 40° = 9x
x = 9 ÷ sin 40°
x = 14.0 cm
sin 58° = 7.6x
x = 7.6 ÷ sin 58°
x = 9.0 cm

Find x to 1 decimal place.

Question 1

x = 13.5 cm

Question 2

x = 15.3 cm

Question 3

x = 9.0 cm

Question 4

x = 13.3 cm

Trigonometry: finding a side with sine worksheet, page 1

Trigonometry: finding a side with sine worksheet, page 2

Answer sheet

  1. A kite flies on a 30 m string, pulled tight. The string makes an angle of 52° with the ground. How high is the kite? Give your answer to 1 decimal place.

    23.6 m

  2. A ramp rises 0.8 m and makes an angle of 4.8° with the ground. How long is the ramp? Give your answer to 1 decimal place.

    9.6 m

  3. A water slide is 40 m long and slopes at 25° to the ground. How high is the top of the slide? Give your answer to 1 decimal place.

    16.9 m

  1. Find the length x to 1 decimal place.

    x = 5.5 cm
    x9 cm38°

  2. Find the length x to 1 decimal place.

    x = 11.4 cm
    5 cmx26°

  3. Label O and H, then find x to 1 decimal place.

    x = 8.8 cm
    x12 cm47°
Exit tickets to print