Geometry Rules & Formulas
Complete guide to sine rule, cosine rule, and triangle formulas
Sine Rule
Essential rules for solving triangles using the sine rule
Sine Rule Formula
a/sin A = b/sin B = c/sin C
Where a, b, c are sides and A, B, C are opposite angles
When to use:
Two angles and one side (AAS or ASA)
When to use:
Two sides and one non-included angle (SSA)
Step-by-Step Process
Step 1: Identify known values
List the given sides and angles
Step 2: Choose appropriate formula
Select the sine rule variation needed
Step 3: Substitute and solve
Plug in values and calculate
Cosine Rule
Essential rules for solving triangles using the cosine rule
Cosine Rule Formula
c² = a² + b² - 2ab cos C
Where c is the side opposite angle C
When to use:
Three sides (SSS) - find angles
When to use:
Two sides and included angle (SAS)
Alternative Forms
Find side: c² = a² + b² - 2ab cos C
When you have two sides and included angle
Find angle: cos C = (a² + b² - c²) / 2ab
When you have all three sides
Triangle Properties
Essential properties and relationships in triangles
Angle Sum
A + B + C = 180°
Sum of angles in any triangle
Area Formula
Area = ½ab sin C
Area using two sides and included angle
Pythagorean Theorem
a² + b² = c²
For right-angled triangles only
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