Question

A ship sailed 3 km west, then 2 km south.

A) Give its three-figure bearings from an observer who stayed at its starting point
to the nearest degree.
looking back
B) For a person on the ship, what would be the three-figure bearings,
to the starting point?

Answer 1

Check the picture below.

let's recall to get the bearings we always start from the North line and move clockwise, so for a person at the starting point, that bearing will be 180° + 56.31°, so we can round that up to 236°.

For a person in the ship, well, that's 56.31°, rounded up to 056°.

how did we get 33.69°?

`\tan(\theta )=\cfrac{\stackrel{opposite}{2}}{\underset{adjacent}{3}} \implies \tan^(-1)(~~\tan( \theta )~~) =\tan^(-1)\left( \cfrac{2}{3} \right) \\\\\\ \theta =\tan^(-1)\left( \cfrac{2}{3} \right)\implies \theta \approx 33.69^o`