Trigonometry – Non-Right-Angled Triangles

Students learn how to derive the Sine, Cosine and Area formulae for non-right-angled triangles.  They use this knowledge to solve complex problems involving triangular shapes.

This unit takes place in Term 5 of Year 10 and follows on from trigonometry with right-angled triangles.


Trigonometry – Non-Right-Angled Triangles Lessons
Revision Lessons


Prerequisite Knowledge

  • Know the trigonometric ratios Sinϑ = Opp/Hyp, Cosϑ = Adj/Hyp and Tanϑ = Opp/Adj.
  • Apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

Success Criteria

  • Know and apply the sine rule [latex]\frac { a }{ SinA } =\frac { b }{ SinB } =\frac { c }{ SinC } [/latex] and cosine rule a2 = b2 + c2 – 2bcCosA to find unknown lengths and angles.
  • Know and apply the formula for the area of a triangle [latex]A=\frac { 1 }{ 2 } abSinC[/latex] to calculate the area, sides or angles of any triangle.


Key Concepts

  • The Sine rule is used when:
    • Any two angles and a side is known.
    • Any two sides and an angle is known
  • The Cosine rule is used when:
    • all three sides are known
    • two sides and the adjoining angle is known
  • Students should have the opportunity to derive the three formulae from first principals.
  • This topic is often linked with problems involving bearings and map sketches.

Common Misconceptions

  • Students often have difficulty choosing the correct formula.
  • A common mistake is attempting to use Pythagoras’ Theorem to find a length in a non-right angled triangle.
  • Marks are often lost when breaking down the Cosine Rule using the order of operations.

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