Sine, cosine, tangent

problem

Sine and Cosine for Connected Angles

Age

14 to 16

Challenge level

2 out of 3

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.
problem

Flight Path

Age

16 to 18

Challenge level

2 out of 3

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
problem

Raising the Roof

Age

14 to 16

Challenge level

2 out of 3

How far should the roof overhang to shade windows from the mid-day sun?
problem

Pumping the Power

Age

16 to 18

Challenge level

2 out of 3

What is an AC voltage? How much power does an AC power source supply?
problem

At a Glance

Age

14 to 16

Challenge level

3 out of 3

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

Circumnavigation

Age

14 to 16

Challenge level

3 out of 3

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
problem

Circle Scaling

Age

14 to 16

Challenge level

3 out of 3

Describe how to construct three circles which have areas in the ratio 1:2:3.
problem

Pythagoras on a Sphere

Age

16 to 18

Challenge level

3 out of 3

Prove Pythagoras' Theorem for right-angled spherical triangles.
problem

Lying and Cheating

Age

11 to 14

Challenge level

2 out of 3

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
problem

Dodecawhat

Age

14 to 16

Challenge level

1 out of 3

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.