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Overbearing

Stage: 3 Short Challenge Level: Challenge Level:1

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 $210$.


This problem is taken from the UKMT Mathematical Challenges.

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