GCSE · Pythagoras & right-angled trigonometry

Right-angled trigonometry (SOHCAHTOA)Exam-style questions

Labelling opposite, adjacent and hypotenuse from the angle you are using, choosing the right ratio, finding sides and angles, where the exact values come from, and angles of elevation and depression.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    In triangle PQRPQR, the line PSPS is perpendicular to QRQR.9.6 cm47°29°PQRSPQ=9.6PQ = 9.6 cm \qquad angle PQS=47°PQS = 47° \qquad angle PRS=29°PRS = 29°

    Calculate the length of PRPR.

    Give your answer correct to 1 decimal place.

    (3 marks)
    Level 4 · 3 marksTry it
  2. 2
    The diagram shows a right-angled triangle.7.5 cmx34°Diagram NOT accurately drawn

    Work out the length of xx. Give your answer correct to 1 decimal place.
    Level 4 · 3 marksTry it
  3. 3
    The diagram shows a right-angled triangle.x11 cm52°Diagram NOT accurately drawn

    Work out the value of xx. Give your answer correct to 3 significant figures.
    Level 4 · 3 marksTry it