The General Triangle — The Navigator
Sine Rule · Cosine Rule · Area Formula
Phase 1: Anchor: Right-Angle Review (SOH CAH TOA)
Panel A — The Triangle Breaker
Live Area
19.50 unit²
½ab·sin C
19.50 unit²
∠ Sum
180.0°
Panel B — Logic Track
The Decision Tree
Look at what you know. Do you have a 'Matching Pair' (an angle + the side directly opposite it)? If YES → Sine Rule. If NO, but you have two sides and the angle TRAPPED between them (SAS) → Cosine Rule. Three sides (SSS)? Also Cosine Rule.
📐 SOH CAH TOA Refresher
Sin θ = Opposite / Hypotenuse
Cos θ = Adjacent / Hypotenuse
Tan θ = Opposite / Adjacent
Drag vertices until one angle ≈ 90° to see SOH CAH TOA activate!
⚠ Examiner Trap
SOH CAH TOA only works for RIGHT-ANGLED triangles. If there is no right angle, you MUST use Sine Rule or Cosine Rule.
Live Triangle Data
Side a (BC):
6.82
Side b (AC):
6.82
Side c (AB):
6.50
Angle A:
61.6°
Angle B:
61.6°
Angle C:
56.9°
Panel C — Dynamic Solver
Cosine Rule: Find a Missing Side
Two sides and included angle
Formula
a² = b² + c² − 2bc·cos(A)
Answer
a = 7.00
Gen Z Study · Edexcel 4MA1 Spec A · Sine & Cosine Rules · Limitless Lesson
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