# Angles, Triangles and Trigonometry - June 2007, Stage 2&3

## Problems

### How Safe Are You?

##### Stage: 2 Challenge Level:

How much do you have to turn these dials by in order to unlock the safes?

### Six Places to Visit

##### Stage: 2 Challenge Level:

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

### Number the Sides

##### Stage: 2 Challenge Level:

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

### Dotty Circle

##### Stage: 2 Challenge Level:

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

### Round and Round and Round

##### Stage: 3 Challenge Level:

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

### Can You Explain Why?

##### Stage: 3 Challenge Level:

Can you explain why it is impossible to construct this triangle?