Question : If the angle of elevation of a cloud from a point 200 m above a lake is $30^\circ$ and the angle of depression of its reflection in the lake is $60^\circ$. Then the height of the cloud above the lake is:

Option 1: 100 m

Option 2: 200 m

Option 3: 300 m

Option 4: 400 m

Question : The angle of elevation of an aeroplane as observed from a point 30 metres above the transparent water surface of a lake is 30° and the angle of the depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water surface of the lake is:

Option 1: 60 metres

Option 2: 45 metres

Option 3: 50 metres

Option 4: 75 metres

Question : From the top of a 20 metres high building, the angle of elevation from the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is: $(\sqrt{3} = 1.732)$

Option 1: 45.46 metres

Option 2: 45.64 metres

Option 3: 54.64 metres

Option 4: 54.46 metres

Question : The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar raised so that its angle of elevation at the same point may be 45°, is:

Option 1: 63.4

Option 2: 86.6

Option 3: 126.8

Option 4: 173.2