 Applications of Bearings

Lesson

Example 1 A slightly lost hiker walks $300$300 m east before turning south walking another $800$800 m. What is its true bearing from its original position (to $1$1 decimal place)? And then what is this as a compass bearing?

Think: to do this questions a diagram is a great way to start.  This is the diagram I drew. The angle we want to find is in green.  It is equal to 90° + the angle inside the triangle that I can find using trigonometry.

Do: Bearing is

 $90+\tan^{-1}\frac{800}{300}$90+tan−1800300​ $=$= $90+\tan^{-1}\frac{8}{3}$90+tan−183​ $=$= $90+69.44$90+69.44 $=$= $159.44$159.44

and to 1 decimal place the final bearing is $159.4$159.4°N

As a compass bearing we need to know the acute angle with the North South line.  This is $180-159.4=20.6$180159.4=20.6

The compass points we will use will be South first, and then East, so the compass bearing is S$20.6$20.6°E

Example 2

The position of a ship S is given to be $20$20 kilometres from P, on a true bearing of $0$0$49$49$^\circ$°T.

The position of the ship can also be given by its $\left(x,y\right)$(x,y) coordinates. 1. If the ship's $x$x-coordinate is $x$x, find $x$x to one decimal place.

2. If the ship's y-coordinate is $y$y, find $y$y to one decimal place.