Sine Rule

Summary

The sine rule is used to calculate unknown sides and angles in triangles that are not right-angled. It can also be used to calculate the area of a non-right-angled triangle using the sine ratio.

• Sine Rule — a formula used to find unknown sides or angles in any triangle, not just right-angled ones. Example: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Non-right-angled Triangle — a triangle that does not have a 90-degree angle. Example: A triangle with angles of 50°, 60°, and 70°.
• Opposite Pairs — sides and angles that are opposite each other in a triangle. Example: In triangle ABC, side a is opposite angle A.

Exam Tips

Key Definitions to Remember

• Sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Opposite pairs: Sides and angles that are directly opposite each other in a triangle

Common Confusions

• Using the sine rule in right-angled triangles instead of non-right-angled triangles
• Mixing up which sides and angles are opposite each other

Typical Exam Questions

• Find the length of a side using the sine rule? Use the formula $\frac{a}{\sin A} = \frac{b}{\sin B}$ and solve for the unknown side.
• Calculate an angle using the sine rule? Rearrange $\frac{a}{\sin A} = \frac{b}{\sin B}$ to solve for the unknown angle.
• Find the area of a non-right-angled triangle using the sine ratio? Use the formula $\text{Area} = \frac{1}{2}ab\sin C$.

What Examiners Usually Test

• Ability to correctly apply the sine rule to find unknown sides or angles
• Understanding of when to use the sine rule versus other trigonometric rules
• Correct identification of opposite pairs in a triangle