Question : Two points P and Q are at the distance of $x$ and $y$, where $y>x$, respectively from the base of a building and on a straight line. If the angles of elevation on the top of the building from points P and Q are complementary, then what is the height of the building?

Option 1: $xy$

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

Option 3: $\sqrt\frac{x}{y}$

Option 4: $\sqrt{xy}$

Question : Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 metres, the distance between the two men is: (take $\sqrt{3}=1.732$)

Option 1: $136.6$ metres

Option 2: $50\sqrt{3}$ metres

Option 3: $100\sqrt{3}$ metres

Option 4: $135.5$ metres

Question : On the ground, there is a vertical tower with a flagpole on its top. At a point 9 metres away from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30°, respectively. The height of the flagpole is:

Option 1: $5\sqrt{3}$ metres

Option 2: $6\sqrt{3}$ metres

Option 3: $6\sqrt{2}$ metres

Option 4: $6\sqrt{5}$ metres

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 : A 1.6 m tall observer is 45 metres away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in metres is: (Take$\sqrt{3}=1.732$)

Option 1: 25.98

Option 2: 26.58

Option 3: 27.58

Option 4: 27.98