Weekly Problem 33 - 2009

We are given:

Diagram of information given in question

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

More angles marked in

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

solution

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