GCSE right-angled trigonometry practice and worked examples
Choose sine, cosine or tangent from the sides involved. Practise finding a missing side and an acute angle, then apply the same ideas in contexts.
Foundation and Higher · Useful near the top of Foundation and for Higher revision. Later questions combine steps.
Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.
Higher extension. More demanding selections are marked Higher extension: practice questions 2, 4, 5. Use these after the core work, following your teacher’s guidance.
2 worked examples and 8 original practice questions · Allow 25–40 minutes · Read online or print. Higher extensions are labelled. No account or email needed.
Printing includes the method, examples and space for working, followed by a separate answer section.
A useful approach
Label opposite, adjacent and hypotenuse relative to the angle you are using.
Choose sin = opposite/hypotenuse, cos = adjacent/hypotenuse or tan = opposite/adjacent.
Rearrange before calculating. Use inverse trig for an angle and check your calculator is in degrees.
A mistake to watch for
The opposite and adjacent sides depend on the chosen angle. The hypotenuse is always opposite the right angle.
Learn each method, then practise it
Read each line of working and explain why it follows from the previous line.
Find a missing side
Label opposite, adjacent and hypotenuse relative to the chosen angle. Select sine, cosine or tangent and rearrange before using the calculator in degrees.
In triangle ABC, angle ABC = 90° and angle BAC = 34°.
AB = 12 cm.
Work out the length of BC.
Give your answer correct to 3 significant figures.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle ABC, angle ABC = 90 degrees and angle BAC = 34 degrees. AB = 12 cm. Work out the length of BC. Give your answer correct to 3 significant figures. Use the labelled information; do not estimate measurements from the sketch.
BC is opposite the 34° angle and AB = 12 cm is adjacent to it, so use tan.
tan 34° = BC ÷ 12.
BC = 12 × tan 34° = 12 × 0.6745... = 8.094... = 8.09 cm (3 sf).
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle DEF, angle DEF = 90 degrees. DE = 10 cm and EF = 7 cm. Work out the size of angle FDE. Give your answer correct to 1 decimal place. Use the labelled information; do not estimate measurements from the sketch.
EF = 7 cm is opposite angle FDE and DE = 10 cm is adjacent to it, so use tan.
Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.
In triangle PQR, angle PQR = 90° and angle PRQ = 52°.
PQ = 9 cm.
Work out the length of PR.
Give your answer correct to 3 significant figures.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle PQR, angle PQR = 90 degrees and angle PRQ = 52 degrees. PQ = 9 cm. Work out the length of PR. Give your answer correct to 3 significant figures. Use the labelled information; do not estimate measurements from the sketch.
In triangle RST, angle RST = 90° and angle SRT = 41°.
RT = 20 cm.
Calculate the length of RS.
Give your answer correct to 3 significant figures.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle RST, angle RST = 90 degrees and angle SRT = 41 degrees. RT = 20 cm. Calculate the length of RS. Give your answer correct to 3 significant figures. Use the labelled information; do not estimate measurements from the sketch.
A ladder of length 6 m leans against a vertical wall.
The ladder makes an angle of 68° with the horizontal ground.
Work out how far up the wall the ladder reaches.
Give your answer correct to 3 significant figures.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. A ladder of length 6 m leans against a vertical wall. The ladder makes an angle of 68 degrees with the horizontal ground. Work out how far up the wall the ladder reaches. Give your answer correct to 3 significant figures. Use the labelled information; do not estimate measurements from the sketch.
In triangle ABC, D is the point on AC such that BD is perpendicular to AC.
Angle BAD = 40°, AD = 7 cm and angle BCD = 55°.
Work out the length of BC.
Give your answer correct to 3 significant figures.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle ABC, D is the point on AC such that BD is perpendicular to AC. Angle BAD = 40 degrees, AD = 7 cm and angle BCD = 55 degrees. Work out the length of BC. Give your answer correct to 3 significant figures. Use the labelled information; do not estimate measurements from the sketch.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle JKL, angle JKL = 90 degrees. JK = 5 cm and JL = 13 cm. Work out the size of angle KJL. Give your answer correct to 1 decimal place. Use the labelled information; do not estimate measurements from the sketch.
Work out the size of angle BAC. Give your answer correct to 1 decimal place.
Write down the size of angle BCA, correct to 1 decimal place.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle ABC, angle ABC = 90 degrees. AB = 15 cm and BC = 8 cm. Work out the size of angle BAC. Give your answer correct to 1 decimal place. Write down the size of angle BCA, correct to 1 decimal place. Use the labelled information; do not estimate measurements from the sketch.
In triangle ABC, angle ABC = 90° and angle BAC = 27°. AB = 11 cm.
Work out the length of BC. Give your answer correct to 3 significant figures.
In triangle PQR, angle PQR = 90°. PQ = 9 cm and PR = 14 cm.
Work out the size of angle PRQ. Give your answer correct to 1 decimal place.
Diagram for SOHCAHTOA (Trigonometry). The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. In triangle ABC, angle ABC = 90 degrees and angle BAC = 27 degrees. AB = 11 cm. Work out the length of BC. Give your answer correct to 3 significant figures. In triangle PQR, angle PQR = 90 degrees. PQ = 9 cm and PR = 14 cm. Work out the size of angle PRQ. Give your answer correct to 1 decimal place. Use the labelled information; do not estimate measurements from the sketch.
Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.
Answer 1
Show answer and working for question 1
PQ = 9 cm is opposite the 52° angle and PR is the hypotenuse, so use sin.
sin 52° = 9 ÷ PR.
PR = 9 ÷ sin 52° = 9 ÷ 0.7880... = 11.42... = 11.4 cm (3 sf).
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