M4.3.7 For the adult
The sine rule and the cosine rule
A triangle has no right angle. You know two of its angles and one side. How can you find the other sides?
What this chapter teaches
The sine rule and the cosine rule work in every triangle, not only right angled ones. Both come from cutting a triangle with its height. The sine rule needs a matching pair of an angle and the side opposite it, and it can give two answers for an angle. The cosine rule is for two sides and the angle between, or for three sides.
Three questions to ask
There is no one right wording. Listen for the idea.
- How does the height of a triangle lead to the sine rule?
- How do you decide between the sine rule and the cosine rule?
- Why can the sine rule give two angles, and when does the second one fit?
After the chapter, the learner can
- Use the sine rule to find a side or an angle
- Use the cosine rule when you know two sides and the angle between
What they copy into their notebook
Sine rule: a ÷ sin A = b ÷ sin B. Use it with a matching pair. Cosine rule: a² = b² + c² − 2bc cos A. Use it with two sides and the angle between, or three sides.