Pythagoras’ Theorem and Trigonometry In 3D
6.3 Non-right-angled triangles – Cheat Sheet
Sine Rule
a / sinA = b / sinB = c / sinC
Find a side: a = (sinA × b) / sinB
Find an angle: A = sin⁻¹( (a × sinB) / b )
Cosine Rule
Finding a side: a² = b² + c² − 2bc × cosA
Finding an angle: cosA = (b² + c² − a²) / (2bc)
Area of a Triangle
Area = ½ab × sinC
Works for any triangle when two sides and the included angle are known.
Ambiguous Case (SSA)
When using the sine rule for angles:
If A = sin⁻¹(value), another possible solution is A’ = 180° − A.
Check which fits the triangle.
Formulas Table
Find side (Sine Rule): a = (sinA × b) / sinB
Find angle (Sine Rule): A = sin⁻¹( (a × sinB) / b )
Find side (Cosine Rule): a² = b² + c² − 2bc × cosA
Find angle (Cosine Rule): cosA = (b² + c² − a²) / (2bc)
Area: ½ab × sinC