LearnRoost.Playground
← All visuals GCSE Higher & A-level Maths

Sine rule, cosine rule & ½ab sin C area

Choose which measurements are given, or drag the triangle vertices directly on the canvas. The page picks the right rule, solves the triangle step by step, calculates the area using ½ab sin C, and draws both triangles in the ambiguous sine-rule case (SSA).

What's given:
Drag vertex C or B to reshape the triangle Use Cosine Rule: c² = a² + b² − 2ab cos C
Given measurements (SAS: side a, side b, included angle C)

1. Which rule should I use?

Cosine rule (side)

2. Step-by-step working

Solved

3. Area of the triangle (½ab sin C)

Area = 22.9 cm²

Dropping perpendicular height h = b sin C from vertex A onto base a gives Area = ½ × base × height = ½ab sin C (works with any two sides and their included angle).