You may also like

problem icon

Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

problem icon

Tri-split

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

problem icon

Polycircles

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Trigonometric Protractor

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.