Question : Let A and B be two towers with the same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of a and b are 30^o and 45^o, respectively. The ratio of the heights of A and B is:

Option 1: $1: 3$

Option 2: $1: \sqrt{3}$

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

Option 4: $3: 1$

Question : If the angle of elevation of a balloon from two consecutive kilometre stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be:

Option 1: $\frac{\sqrt{3}}{2}$ km

Option 2: $\frac{1}{2}$ km

Option 3: $\frac{2}{\sqrt{3}}$ km

Option 4: $3\sqrt{3}$ km

Question : Two posts are 2 metres apart. Both posts are on the same side of a tree. If the angles of depressions of these posts when observed from the top of the tree are 45° and 60° respectively, then the height of the tree is:

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

Option 2: $(3+\sqrt{3})$ metres

Option 3: $(-3+\sqrt{3})$ metres

Option 4: $(3-\sqrt{2})$ metres

Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is:

Option 1: $20(\sqrt{3}-1)$ m

Option 2: $20(\sqrt{3}+1)$ m

Option 3: $10(\sqrt{3}-1)$ m

Option 4: $10(\sqrt{3}+1)$ m

Question : From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60° and 30°, respectively. The height (in km) of the aeroplane from the road at that instant, is:

Option 1: $\frac{\sqrt{3}}{2}$

Option 2: $\frac{\sqrt{3}}{3}$

Option 3: $\frac{\sqrt{3}}{4}$

Option 4: $\sqrt{3}$