Question

As observed form the top of a lighthouse, 100m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° and 60°. Determine the distance travelled by the ship during the period of observation.

Answer 1

Let OA be the lighthouse and B and C be the positions of the ship.

Thus, we have:

OA = 100m, \(\angle OBA\) = 30° and \(\angle OCA\) = 60°

Let

OC = xm and BC = ym

In the right \(\triangle OAC\), we have

∴ Distance travelled by the ship during the period of observation = B = y = 115.47m