JAMB 2000 · UME · Q26

Elevation, depression & bearings

A ship sails a distance of 50 km in the direction S $50^\circ$ E and then 50 km in the direction N $40^\circ$ E. Find the bearing of the ship from its original position.

Worked solution (try it first)

As three-figure bearings, S $50^\circ$ E is $130^\circ$ and N $40^\circ$ E is $040^\circ$ .
They differ by $90^\circ$ , so the two legs meet at a right angle.
The legs are equal, so the triangle is isosceles and the line back to the start makes $45^\circ$ with the first leg.
Turning $45^\circ$ from $130^\circ$ towards the second leg gives $085^\circ$ , which is N $85^\circ$ E, option D.

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