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Trigonometry - Higher

Finding the length of the opposite side


Find the length of side BC.

image: 7cm traingle

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  • We are given angle A and side AB.
  • AB is the hypotenuse.
  • BC is opposite angle A.
  • Therefore we use the formula:
  • sin = opposite / hypotenuse
  • sin 30 = BC / 7
  • Multiply both sides by 7
  • 7 x sin30 = BC
  • Using a calculator we get
  • BC = 3.5cm

Now you try this one.


Find length of side PQ, giving your answer correct to 3 sf.

image: triangle

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The answer is 4.77cm (3 sf).

  • Can you see that PQ is opposite the given angle and that QR is adjacent to it?
  • Use the formula:
  • tan = opposite / adjacent
  • tan50 = PQ / 4
  • 4 × tan50 = PQ
  • PQ = 4.77 (3 sf)

Back to Geometry and measures index

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