Triangles: sine rule, cosine rule, SOH CAH TOA

Solve right-angled triangles, then any triangle, and draw it to scale. About 11 minutes, GCSE / A-level.

What you will do

  1. Right-angled triangles. Label the sides from the angle you care about: opposite, adjacent and hypotenuse. Then = OH, = AH, = OA (SOH CAH TOA).
  2. A ladder against a wall. A 10 m ladder at 65° to the ground: the height up the wall is the opposite side, so use sine.
  3. The cosine rule. For two sides and the angle between them: c^2 = a^2 + b^2 - 2ab C.
  4. The sine rule. When you know an angle and the side opposite it, the ratio a A is the same for every side.
  5. Three sides only. With all three sides, rearrange the cosine rule to find each angle.

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