### 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?

### Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

# Cosines Rule

##### Stage: 4 Challenge Level:

Why is the $60$ degree angle opposite the side of median length?

For the second part all you need is the cosine formula and some algebraic manipulation to get the required result.