The captain of a ship sailing along a bearing of 070oT observes two lighthouses in a line due North of himself. The ship continues on the same course for a further 5 km. Now, one of the lighthouses has a bearing of 280oT from the ship and the other has a bearing of 320oT from the ship. Calculate the distance between the lighthouses.

Question

The captain of a ship sailing along a bearing of 070oT observes two lighthouses       in a line due North of himself.      The ship continues on the same course for a further 5 km. Now, one of the lighthouses       has a bearing of 280oT from the ship and the other has a bearing of 320oT from the ship.      Calculate the distance between the lighthouses.

Steve · Answer

draw a diagram. If the two lighthouses are at S and N, and the ship moved from A to B, then let the east-west distance moved by the ship be x. x = 5cos20° SN = x tan50° - x tan10°