Using the Sine Rule to find missing sides

Use matching opposite side-angle pairs in the Sine Rule to calculate missing side lengths 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
  • included angle
  • degrees
  • significant figures

Task goals

  • Identify which side is opposite each labelled angle.
  • Select a complete known side-angle pair before substituting into the Sine Rule.
  • Rearrange the Sine Rule to calculate a missing side.
  • Find a third angle first when it is needed to form the required opposite pair.
  • Round final side lengths to the stated accuracy and include units.
  • Use the Sine Rule more than once to calculate two missing sides or a perimeter.

Where this fits

What leads into this objective, and where it goes next.

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Using the Sine Rule to find missing sides

Using the Sine Rule to find missing sides

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