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The cosine rule

Geometry · Grade 7–9

Strand: Geometry Substrand: Trigonometry Sparx code: U591 Sparx levels: 4, 5 Tier: Higher Only

Key steps (method)

  • Draw and label the right-angled triangle (mark the right angle).
  • Pick the trig ratio using SOHCAHTOA based on the sides you know/need.
  • Substitute values and solve (use inverse trig for angles).
  • Round appropriately (usually 1 d.p. for lengths, 1 d.p. for angles unless told otherwise).
  • Check: does the angle/length look sensible for the triangle?

Common mistakes

  • Choosing the wrong sides (opposite/adjacent relative to the angle).
  • Using sin/cos/tan on a non-right-angled triangle (unless using sine/cosine rule, etc.).
  • Calculator in the wrong mode (degrees vs radians).
  • Rounding too early.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of The cosine rule (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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