Sine & cosine rule
Edexcel GCSE Maths revision on Sine & cosine rule. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
In a triangle ABC, if you know two sides and the included angle, which rule should you use to calculate the third side?
- A) The cosine rule because it links three sides to one angle
- B) The sine rule formula because it links two sides to one
- C) The tangent method because it links two sides to one
- D) The Pythagoras rule because it links three sides to one
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Answer: The cosine rule because it links three sides to one angle
The cosine rule is used for finding a side when two sides and the included angle are known. The sine rule is typically used for side-angle pairs, while Pythagoras' theorem only applies to right-angled triangles.
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Question 2
What is the length of side x in a triangle where angle A is 60 degrees, side b is 5 cm, and side c is 8 cm?
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Answer: 7
Using the cosine rule, x squared equals 5 squared plus 8 squared minus 2 times 5 times 8 times cos(60). This simplifies to 25 plus 64 minus 40, which is 49, so x equals 7.
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Question 3
Which condition is required to use the sine rule to find an unknown side in a triangle?
- A) One side and its opposite angle must be known
- B) Two sides and the included angle are given
- C) All three sides of the triangle are known
- D) Two angles and the adjacent side are known
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Answer: One side and its opposite angle must be known
The sine rule requires a 'matching pair' of a side and its opposite angle to establish the ratio. Without this pairing, you cannot solve for an unknown side using the sine rule alone.
Want to test yourself on the remaining cards for this topic?
13 more questions on Sine & cosine rule — plus mistakes tracking and spaced repetition across the whole Maths spec.