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. . . .
What are the shortest distances between the centres of opposite
faces of a regular solid dodecahedron on the surface and through
the middle of the dodecahedron?
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.
Can you explain what is happening and account for the values being
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
There are many different methods to solve this geometrical problem - how many can you find?
Prove Pythagoras' Theorem for right-angled spherical triangles.
Find the exact values of some trig. ratios from this rectangle in
which a cyclic quadrilateral cuts off four right angled triangles.
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