Triangles: sine and cosine rules: watch it solved step by step

Solve any triangle with the sine and cosine rules, or a right-angled one with SOH CAH TOA and Pythagoras, with a scale drawing. Level: GCSE / A-level. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: A = 40, B = 60, a = 8

  1. Understanding the problem. Three measurements of a triangle are known. Sides are written in small letters (a, b, c) and each is opposite the capital-letter angle (A, B, C). This is the AAS case.
  2. The rules. The cosine rule links three sides and one angle. The sine rule links two sides and their opposite angles.
  3. Angle C. The angles add up to 180°.
  4. The sine rule constant. One side and its opposite angle give the constant a/ A, the same for every side of the triangle.
  5. Side b. Multiply the constant by sin B.
  6. Side c. Multiply the constant by sin C.
  7. Check. The angles must add to 180°, and the largest side must face the largest angle.

Answer: a = 8, b = 10.78, c = 12.26; A = 40°, B = 60°, C = 80°

Practise triangles: sine and cosine rules with problems the Lab marks for you.

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