Sine rule: GCSE and IGCSE Maths Practice | Revision Workshop
Non-Right Angled Trigonometry
Sine rule
32 self-marking GCSE and IGCSE practice questions on Sine rule, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Instant marking with full worked solutions on every question.
A few of the 32 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 6-7
In triangle ABC, angle B = 30°, side b = 19.8 cm (the side opposite angle B), and angle C = 54°. Work out the length of side c (the side opposite angle C). Give your answer correct to 1 decimal place.
Show the worked solution
sinCc=sinBb
What are the common mistakes in Sine rule?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Uses the cosine rule where the sine rule was the correct method, or vice versa
Tried to apply the cosine rule when only one side and two angles are known - the sine rule is the correct tool, using the calculated third angle to complete a matching side/angle pair
Uses the wrong angle because the required angle-sum step was skipped
Paired side a with angle B instead of first calculating angle C (180°−30°−56°=94°) - side c is opposite angle C, not angle B, so the missing angle must be found first
Inverts the ratio when substituting into the sine rule
Set up the ratio the wrong way round - each side must be paired with the sine of its OWN opposite angle, not the other angle
Quick answers about Sine rule
How many Sine rule practice questions are there?
There are 32 self-marking GCSE and IGCSE Maths questions on Sine rule, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Sine rule?
No. You can start practising Sine rule straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
M1
c=sin30°19.8×sin54°=32 cm (to 1 d.p.) A1
Question 21 markGrade 7-8
In a triangle, side length 54 is opposite a 31° angle, and angle x is opposite a side that is opposite a 72° angle.
Leah tries to use the sine rule to find angle x. Here are the first two lines of her working:
sin(31°)x=sin(72°)54x=sin(72°)54sin(31°)
What error has Leah made in this working?
Show the worked solution
In the sine rule sinAa=sinBb, each side is paired with the angle OPPOSITE it. Leah is trying to find angle x
Question 33 marksGrade 7-8
Priya, an engineer, is measuring a triangular plot of land ABC. Angle A = 30°, angle B = 56°, and side a = 19.8 m (the side opposite angle A). Work out the length of side c (the side opposite angle C). Give your answer correct to 1 decimal place.
Question 43 marksGrade 7-8
Kai, a sailor, is measuring a triangular bay ABC. Angle A = 80°, angle B = 53°, and side a = 12.3 m (the side opposite angle A). Work out the length of side c (the side opposite angle C). Give your answer correct to 1 decimal place.
Question 53 marksGrade 7-8
Ryan, a surveyor, is measuring a triangular field ABC. Angle A = 50°, angle B = 42°, and side a = 7.3 m (the side opposite angle A). Work out the length of side c (the side opposite angle C). Give your answer correct to 1 decimal place.
Question 63 marksGrade 7-8
Leon, a hiker, is measuring a triangular valley ABC. Angle A = 53°, angle B = 69°, and side a = 20 m (the side opposite angle A). Work out the length of side c (the side opposite angle C). Give your answer correct to 1 decimal place.
The correct setup should be: 54sin(x)=[the side opposite x]sin(72°) (or an equivalent correctly-paired ratio) - Leah has incorrectly treated x as if it were a length to solve for directly, rather than as an angle inside a sine function.