# 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.

##### 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 and cosine rule a2 = b2 + c2 – 2bcCosA to find unknown lengths and angles.
• Know and apply the formula for the area of a triangle 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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