Question : The distance between the two pillars is 120 metres. The height of one pillar is three times the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is:

Option 1: 34.64

Option 2: 51.96

Option 3: 69.28

Option 4: 103.92

Question : Two posts are $x$ metres apart and the height of one is double that of the other. If, from the midpoint of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height (in metres) of the shorter posts is:

Option 1: $\frac{x}{2\sqrt{2}}$

Option 2: $\frac{x}{4}$

Option 3: $x\sqrt{2}$

Option 4: $\frac{x}{\sqrt{2}}$

Question : The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

Option 1: 4 metres

Option 2: 7 metres

Option 3: 9 metres

Option 4: 6 metres

Question : If the angle of elevation of the top of a pillar from the ground level is raised from 30° to 60°, the length of the shadow of a pillar of height $50\sqrt{3}$ metres will be decreased by:

Option 1: 60 metres

Option 2: 75 metres

Option 3: 100 metres

Option 4: 50 metres

Question : Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are $30^{\circ}$ and $45^{\circ}$, respectively, at a point on the road between the pillars. What is the distance (in m ) of the point from the foot of pillar A?

Option 1: $40(\sqrt{3}-1)$

Option 2: $20(2-\sqrt{3})$

Option 3: $20(3-\sqrt{3})$

Option 4: $39 \sqrt{3}$

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