M4.3.3 For the adult
Opposite, adjacent and hypotenuse
Two right angled triangles have the same angles, but one is twice as big. Is opposite ÷ adjacent bigger in the big one?
What this chapter teaches
Once an acute angle θ is chosen, the sides of a right angled triangle are named from it: opposite faces θ, adjacent touches it, and the hypotenuse faces the right angle. For a fixed angle, opposite ÷ adjacent is the same in every size of triangle, because all such triangles are enlargements of each other.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you find the opposite side if the page is turned upside down?
- Why does opposite ÷ adjacent stay the same when the triangle gets bigger?
- If θ is the other angle, which two sides swap names?
After the chapter, the learner can
- Name the opposite, adjacent and hypotenuse for a given angle
- Show by drawing that opposite ÷ adjacent is fixed for each angle
What they copy into their notebook
Hypotenuse faces the right angle. Opposite faces θ. Adjacent touches θ. For one angle, opposite ÷ adjacent is the same in every size of triangle.