AI generatedGeometry and measuresGCSE Higher

Choosing between sine and cosine rules

Choosing between sine and cosine rules.

  • Label the sides and angles before choosing a rule.
  • Sine rule: matching opposite pairs. Cosine rule: three sides or two sides and the included angle.
  • Use degree mode. Keep full calculator accuracy until the final rounding step.

Example 1

Choose a rule, then find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Pair each side with its opposite angle.Multiply by the sine opposite the unknown side.
CalculatorKeep full accuracy, then round the final result.

Sine rule: a complete opposite side–angle pair is known.

Example 2

Choose a rule and find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Two sides and the included angle require the cosine rule.Substitute carefully, including the subtraction.Take the positive square root.
CalculatorKeep full accuracy, then round the final result.

Your turn

Question 1

Choose a rule, then find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Pair each side with its opposite angle.Multiply by the sine opposite the unknown side.
CalculatorKeep full accuracy, then round the final result.
Question 2

Choose a rule and find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Two sides and the included angle require the cosine rule.Substitute carefully, including the subtraction.Take the positive square root.
CalculatorKeep full accuracy, then round the final result.
Question 3

Choose a rule, then find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Pair each side with its opposite angle.Multiply by the sine opposite the unknown side.
CalculatorKeep full accuracy, then round the final result.
Question 4

Choose a rule and find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Two sides and the included angle require the cosine rule.Substitute carefully, including the subtraction.Take the positive square root.
CalculatorKeep full accuracy, then round the final result.
Question 5

Choose a rule, then find side a. Give your answer to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Pair each side with its opposite angle.Multiply by the sine opposite the unknown side.
CalculatorKeep full accuracy, then round the final result.
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