Overbearing
A village has a pub, church and school. What is the bearing of the school from the church?
Age
11 to 14
Challenge level
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 $210$.