A ship X sailing with velocity (21 km/h, 052°) observes a light from the lighthouse due North. The bearing of the lighthouse from the ship, 20 minutes later, is found to be 312°, calculate correct to three significant figures: (i) the original distance, in kilometres, when the lighthouse is due west of the ship from the time when it is due North of the ship.
(ii) the time, in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
(iii) the distance, in km, of the ship from the lighthouse when the lighthouse is due West of the ship.