Shape and Space 10
3 marks · NormalExplain how to determine whether the sine rule or the cosine rule should be used to solve a triangle. Give an example for each.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Use the sine rule when you know two angles and one side, or two sides and a non-included angle. Use the cosine rule when you know two sides and the included angle, or all three sides. Example: Sine rule - sides a, b and angle A known; Cosine rule - sides a, b, angle C between them known.
Must show: Both rules described with clear conditions, Example for sine rule, Example for cosine rule
Common mistakes: Mixing up included/non-included angle conditions
Show mark scheme and worked solution
Marking points
M1 · 1 mark · States criteria for using sine rule (SSa or AAS cases).
M2 · 1 mark · States criteria for using cosine rule (SAS or SSS cases).
B1 · 1 mark · Provides a valid example for each case (sine and cosine rule).
Worked solution
Use the sine rule when you are given two angles and one side (AAS or ASA) or two sides and an angle not between them (SSA). Example: In triangle ABC, if you know angles A, B and side a, or know sides a, b and angle A, use the sine rule.
Use the cosine rule when you are given two sides and the included angle (SAS) or all three sides (SSS). Example: If you know sides a, b, and angle C between them, use the cosine rule .