Prove Pythagoras' Theorem for right-angled spherical triangles.

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Can you explain what is happening and account for the values being displayed?

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.

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?

There are many different methods to solve this geometrical problem - how many can you find?

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 degrees?

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.

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?