Help needed with tricky maths puzzle question. bearings, degrees, Pythagoras,?

A ship sails from a harbour on a bearing of 072掳 to a buoy 12 Km away. Then it changes direction and sails 20 Km to a lighthouse due East of the harbour.



Answer A: On what bearing does the boat sail from the buoy to the lighthouse (to the nearest degree)?



Answer B: How far is it from the lighthouse back to the harbour?Help needed with tricky maths puzzle question. bearings, degrees, Pythagoras,?
Whoever set that does not know the difference between a Bearing and a Course. Ships do not 'sail on bearings', they 'follow a course'.

Also they do not 'change direction', they 'alter course'.

I do not like Km either. They should be nautical miles.



The angle at the harbour between the ship's initial course and the lighthouse is 18 degrees.

You now have a triangle with 2 sides (12 and 20) and an angle between the 12 side and the unknown distance side (18 degrees).

You can solve what you want using the Sine Rule.



Course from buoy to lighthouse = 102 degrees

Distance lighthouse to harbour = 32Km



It's obviously slightly more than 32 but if you are not giving a totally accurate answer to the course there is no point in giving a totally accurate answer to any other calculated value.Help needed with tricky maths puzzle question. bearings, degrees, Pythagoras,?
A 18 degrees

B following the same route 32Km.

names to match brother