### Why do this problem?

This
problem encourages learners to examine the relationships
between the ratios of corresponding sides of similar right-angled
triangles. The problem extends the ideas established in the
problems

Dotty
Circle and

Where
is the Dot? using these ideas to introduce sine and consine
ratios.

### Possible approach

The suggestions here build on
learners having met the problem " Where is the dot? ". The support notes include an interactivity
which makes the connection between the animation in "Where is the
dot" and the protractor more explicit .

Demonstrate how the protractor works.

Ask the learners to investigate the properties of the protractor
and the numbers that are produced when it is laid over the angles
of each of the right-angled triangles.

What stays the same and what is different?

Working in pairs, ask them to discuss, list and justify what they
notice and try to give explanations for what they find ready to
share ideas with the whole group.

### Key questions

- Why do the numbers remain the same when the protractor is
placed over either of the two acute angles?
- Why don't the numbers change when you change the radius of the
protractor?
- What is the connection between the "lengths of the two adjacent
sides and the "length" of the hypotenuse?
- What relationships remain the same for any triangle? Can you
explain why?

### Possible extension

How could you use the protractor to find angles and sides of
right-angled triangles with an hypotenues that is not one unit
long?

### Possible support

The interactivity below makes explicit the connections between the
problem

Where
is the Dot? and the protractorby showing the lengths of the
horizontal and vertical lines in a circle of unit radius.