Sine, Cosine and Area 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 find the area of a triangle using the sine ratio.

• Sine Rule — a formula used to find unknown sides or angles in any triangle. Example: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Area Rule — a formula to calculate the area of a triangle using the sine of an angle. Example: $\text{Area} = \frac{1}{2}ab\sin C$

Exam Tips

Key Definitions to Remember

• Sine Rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Area Rule: $\text{Area} = \frac{1}{2}ab\sin C$

Common Confusions

• Confusing when to use the sine rule versus the cosine rule.
• Forgetting to use the sine rule only when angles and sides are in opposite pairs.

Typical Exam Questions

• Find the length of the side marked x in a triangle? Use the sine rule to solve for x.
• Find the size of the angle marked θ in a triangle? Use the sine rule and solve for θ, rounding to 1 decimal place.

What Examiners Usually Test

• Correct application of the sine rule in non-right-angled triangles.
• Ability to rearrange the sine rule formula to solve for unknowns.