Question

A ship sails 200 km on a bearing of 243.7 degrees.

(a) How far south has it travelled?
(b) How far west has it travelled?

Answer 1

200 * sin(243.7) ≈ - 179.29 179.29 km to the west
200 * cos (243.7) ≈ - 88.61 88.61 km to the south

Answer 2

Explanation:

The bearing is always measured from the North direction so when we say that the bearing is 243.7 degrees , It means that the ship has sailed in the direction clockwise of North to 243.7 degrees .

a.

When we try to find the distance it has traveled towards south the cos component is used .

so the Ship traveled = 200 cos (243.7) = - 88.61

Negative value represents the opposite direction from North so we say that

Ship has traveled 88.61 km south .

b.

Now the west direction distance can be found by using the sin component

so the distance traveled in the west direction is

200 sin(243.7) =179.30 km

Ship has traveled 179.30 km west .