Discia GCSE Maths › Geometry & Measures › The Sine Rule

The Sine Rule worksheet

6 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

6 questions 23 marks Sheet 1
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  1. 3 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the angle at A, the angle at B and the length of BC given, and AC marked x13 cmx cmABC63°48°Diagram NOT accurately drawn

    Work out the length of \(AC\).

    Give your answer correct to 3 significant figures.

  2. 4 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the angle at A, the angle at B and the length of AB given, and BC marked x7 cmx cmABC60°49°Diagram NOT accurately drawn
    (a)

    Calculate the size of angle \(ACB\).

    (b)

    Calculate the length of \(BC\).

    Give your answer correct to 1 decimal place.

  3. 4 marks

    \(P\) and \(Q\) are two survey markers, \(180\) m apart. A radio mast is at \(R\).

    The angle \(RPQ\) is \(67^\circ\) and the angle \(PQR\) is \(55^\circ\).

    Triangle PQR not accurately drawn, with the baseline PQ and the angles measured at P and at Q given, and QR marked x180 mx mPQR67°55°Diagram NOT accurately drawn

    Work out the distance \(QR\).

    Give your answer correct to the nearest metre.

  4. 5 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the angle at A, the angle at B and the length of AB given and the other two sides unlabelled11 cmABC50°64°Diagram NOT accurately drawn
    (a)

    Work out the size of angle \(ACB\).

    (b)

    Work out the perimeter of the triangle.

    Give your answer correct to 1 decimal place.

  5. 3 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the angle at A, the angle at B and the length of BC given, and AC marked x10 cmx cmABC35°38°Diagram NOT accurately drawn

    Work out the length of \(AC\).

    Give your answer to 3 significant figures.

  6. 4 marks

    \(ABC\) is a triangle.

    Triangle ABC not accurately drawn, with the angle at A, the angle at B and the length of AB given, and BC marked x20 cmx cmABC73°65°Diagram NOT accurately drawn
    (a)

    Work out the size of angle \(ACB\).

    (b)

    Work out the length of \(BC\).

    Give your answer to 1 decimal place.

Answers

  1. \(10.8\ \text{cm}\)
  2. (a) \(71^\circ\)
    (b) \(6.4\ \text{cm}\)
  3. \(195\ \text{m}\)
  4. (a) \(66^\circ\)
    (b) \(31.0\ \text{cm}\)
  5. \(10.7\ \text{cm}\)
  6. (a) \(42^\circ\)
    (b) \(28.6\ \text{cm}\)

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