Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?

Let AB be the observer and CD be the tower. Draw BE CD. Then, CE = AB = 1.6 m, BE = AC = 203 m. DE = tan 30° = 1 BE 3 DE = 203 m = 20 m. 3 CD = CE + DE = (1.6 + 20) m = 21.6 m.
Let AB be the observer and CD be the tower.

Draw BE CD.
Then, CE = AB = 1.6 m,
BE = AC = 20√3 m.

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is