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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.

**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 a
^{2}= b^{2}+ c^{2}– 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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## Sahil Roy says:

<3

Thnks

^^