Weekly Problem 33 - 2009

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 linkingthe 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.

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