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Maths

Trigonometry - Higher

Re-arranging the formula

Question

Find YZ, giving your answer correct to 3 sf

triangle with 25 degree angle

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Answer
  • We are given angle Z
  • XZ is adjacent to angle Z.
  • YZ is the hypotenuse.
  • Therefore we use the formula: cos = adjacent / hypotenuse
  • cos 25 = 5 over YZ

  • This time our unknown side (YZ) is the denominator. If we multiply both sides by YZ, we get:
  • YZ x cos 25 = 5 over YZ x YZ

  • YZ x cos25 = 5
  • Now we can divide both sides by cos25:

    YZ x cos 25 over cos 25 = 5 over 25

  • YZ = 5 over cos 25

  • Using a calculator:
  • YZ = 5 รท 0.9063 = 5.52cm (3 sf)

Look again at the original arrangement of this equation. By rearranging it we have swapped the positions of YZ and cos25. This method works whenever the unknown side is at the bottom of the fraction.

Now have a go at this question, using the above method.

Question

Find PQ, giving your answer correct to 3 sf

image: triangle with 40 degrees

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Answer

The answer is 7.15cm.

We have been given angle Q. Side PR is opposite angle Q and PQ is adjacent to it. We have the opposite and the adjacent so we use the formula:

tan = opposite / adjacent

  • tan40 = 6 / PQ
  • By rearranging the formula we get
  • PQ = 6 / tan40
  • Using a calculator
  • PQ = 7.15 (3 sf)

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