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Year 10 · Trigonometry

Sine rule, cosine rule and area

For triangles without a right angle: sine rule a/sin A = b/sin B, cosine rule c² = a² + b² − 2ab cos C, area ½ab sin C.

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How to do it

  1. Two angles and a side: sine rule.
  2. Two sides and the angle between: cosine rule.
  3. Area: half the product of two sides times the sine of the angle between.

Worked example

In triangle ABC, angle A = 50°, angle B = 35° and a = 10. Find b, to one decimal place.
Sine rule: b / sin B = a / sin A, so b = 10 × sin 35° ÷ sin 50° ≈ 7.5.
Answer: 7.5

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Match each side with the angle opposite it.

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