### Sense of Direction

Weekly Problem 5 - 2012
Can you work out the direction of Abbots Morton from Wyre Piddle?

### Turning N Over

Weekly Problem 34 - 2013
A card with the letter N on it is rotated through two different axes. What does the card look like at the end?

### Kangaroo Hops

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

# Overbearing

##### Stage: 3 Short Challenge Level:

We are given:

We want to find the bearing of the School from the Church, which is the green angle marked on the diagram. We can use the fact that the angles in a triangle sum to $180^\circ$ to mark in some other angles

We know the triangle linking the three buildings is isosceles, so the two missing angles are equal, so are both $30^\circ$.So:

So the green angle is $180^\circ+30^\circ = 210^\circ$, so the bearing of the School from the Church is $210$.

This problem is taken from the UKMT Mathematical Challenges.