Question

4] A ship sails 80 km on a bearing of 55° and then changes course and sails 40 km on

a bearing of 132° By making a scale diagram find: -
a) The final distance of the port from the ship.
b) The final bearing of the port from the ship.

Answer 1

Below

Explanation:

Break each of the legs into vertical and horizontal components so you can add them :

Vertical

80 sin 55 + 40 sin 132 = 95.258 km

Horizontal

80 cos 55 + 40 cos 132 = 19.121 km

Use pythag theorem to calculate the distance from origin

d^2 = 95.258^2 + 19.121^2

show d = 97.16 km from origin

Angle will be arctan ( 95.258/19.121) = 78.65° <====this is the bearing of the SHIP from the PORT....the bearing TO the PORT FROM the ship will be 78.165 + 180 = 258.65°