Using the Sine Rule to find missing angles

Use matching opposite side-angle pairs in the Sine Rule and inverse sine to calculate missing angles in non-right-angled triangles.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM6-6
New NZC (2026)
  • NZC26-P4-GEO-SHP-P-Y10-01

Resources

Terminology

  • Sine Rule
  • opposite side-angle pair
  • non-right-angled triangle
  • inverse sine
  • angle sum of a triangle
  • degrees

Task goals

  • Identify the side opposite each labelled angle.
  • Select a complete known side-angle pair before substituting into the Sine Rule.
  • Rearrange the Sine Rule to make the sine of the missing angle the subject.
  • Use inverse sine to calculate an acute missing angle.
  • Use the angle sum of a triangle to calculate a remaining angle where needed.
  • Round only the final answer and check that the angle size is reasonable for its opposite side.

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Using the Sine Rule to find missing angles

Using the Sine Rule to find missing angles

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