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Trigonometry - Higher

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# Re-arranging the formula

Question

• We are given angle Z
• XZ is adjacent to angle Z.
• YZ is the hypotenuse.
• Therefore we use the formula: cos = adjacent / hypotenuse
• This time our unknown side (YZ) is the denominator. If we multiply both sides by YZ, we get:
• YZ x cos25 = 5
• Now we can divide both sides by cos25:

• Using a calculator:
• YZ = 5 ÷ 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

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:

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

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