# Overbearing

A village has a pub, church and school. What is the bearing of the school from the church?

## Problem

In a village, the pub is $300 \; \text{m}$ due north of the school, and the church is $300 \; \text{m}$ from the pub, at a bearing of $060^\circ$.

What is the bearing of the school from the church?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

We are given:

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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

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

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