Sine Rule and Cosine Rule

These rules are essential for solving non-right-angled triangles (triangles that don't have a 90-degree angle).

Sine Rule

• Formula:

  • a/sin(A) = b/sin(B) = c/sin(C)

  • Where:

    • a, b, and c are the sides of the triangle.

    • A, B, and C are the angles opposite sides a, b, and c, respectively.

• When to Use:

  • When you know:

    • Two angles and one side (AAS or ASA)

    • Two sides and the angle opposite one of them (SSA - but be cautious, this can lead to ambiguous cases)

Cosine Rule

• Formula:

  • a² = b² + c² - 2bc * cos(A)

  • b² = a² + c² - 2ac * cos(B)

  • c² = a² + b² - 2ab * cos(C)

• When to Use:

  • When you know:

    • Three sides (SSS)

    • Two sides and the included angle (SAS)

Key Concepts

• These rules allow you to find missing sides and angles in any triangle, not just right-angled ones.

• The Sine Rule is often used to find missing sides or angles when you have information about angles and opposite sides.

• The Cosine Rule is typically used when you have information about sides and the included angle, or when you know all three sides.