### 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.

# Sine and Cosine for Connected Angles

##### Age 14 to 16Challenge Level
First check that you can find the size of every angle in the diagram.
Next use your knowledge of Sine or Cosine to find calculations for as many lengths as possible.

Remember this is a unit circle, the length $AO$ for example is $1$.