### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

# Trigonometric Protractor

##### Age 14 to 16 Challenge Level:

Draw a right-angled triangle.

Click and drag near the centre of the protractor to move its centre over a vertex of a triangle (not at the right angle).
Click and drag on the inner circle to rotate it until the blue dot aligns with one of the adjacent sides.
Click and drag the blue dot until it aligns with the hypotenuse.
• What do the numbers refer to?
Click and drag the edge of the protractor to change its radius.
• Why don't the numbers change?
• How might this protractor be useful for finding the lengths of sides of different triangles?
• What do you notice about the numbers when the protractor is placed over each of the two acute angles? Can you explain what you see?
• What is the connection between the "lengths" of the two adjacent sides and the "length" of the hypotenuse?
• Do these things remain the same for any triangle? Can you explain why?

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