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Mathematics · Topic

Pythagoras and right-angled trigonometry

Identify opposite, adjacent and hypotenuse before choosing sine, cosine or tangent.

2 original questions in the bank, worth 4 marks · above the two-per-topic floor

Drill this topic All pythagoras and right-angled trigonometry questions

The questions, with the examiner reasoning

Work out3 marksIGCSE

In a right-angled triangle the hypotenuse is 9.6 m. One of the sides next to an angle is 7.2 m. Work out that angle, giving your answer to one decimal place.

Show the mark scheme and the examiner note

Answer: 41.4°

  1. The two sides involved are the adjacent (7.2 m) and the hypotenuse (9.6 m), so use cosine
  2. cos θ = 7.2 ÷ 9.6 = 0.75
  3. θ = 41.4°

Examiner technique: Label opposite, adjacent and hypotenuse on the diagram before choosing a ratio. Most marks lost here are lost to using sine because it was written first on the formula sheet.

Work out1 markBoth boards

A rectangle measures 9 cm by 12 cm. Work out the length of a diagonal.

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Answer: 15 cm

  1. Pythagoras: diagonal² = 9² + 12²
  2. = 225
  3. Diagonal = 15 cm
  • A. 15 cm — Correct: 9² + 12² = 81 + 144 = 225, and √225 = 15.
  • B. 21 cm — That is 9 + 12 — the side lengths added instead of the squares.
  • C. 10.8 cm — Closer to a mis-applied area calculation than to Pythagoras.
  • D. 13 cm — A plausible-looking value. The exact answer is 15, so estimate first: the diagonal must be longer than the longest side.

Examiner technique: The 9-12-15 triangle is a scaled 3-4-5, which appears in papers again and again. Recognising it saves a minute you can spend on a harder question.