An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
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
Can you explain what is happening and account for the values being
The length AM can be calculated using trigonometry in two different
ways. Create this pair of equivalent calculations for different peg
boards, notice a general result, and account for it.
A dot starts at the point (1,0) and turns anticlockwise. Can you
estimate the height of the dot after it has turned through 45
degrees? Can you calculate its height?
The sine of an angle is equal to the cosine of its complement. Can
you explain why and does this rule extend beyond angles of 90
Three squares are drawn on the sides of a triangle ABC. Their areas
are respectively 18 000, 20 000 and 26 000 square centimetres. If
the outer vertices of the squares are joined, three more. . . .
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?