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 : The shadow of a tower standing on a level plane is 40 metres longer when the sun's altitude is 45°, than when it is 60°. The height of the tower is:

Option 1: $30(3+\sqrt{3})$ metres

Option 2: $40(3+\sqrt{3})$ metres

Option 3: $20(3+\sqrt{3})$ metres

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

Question : If the height of a pole is $2\sqrt{3}$ metres and the length of its shadow is 2 metres, then the angle of elevation of the sun is:

Option 1: 90°

Option 2: 45°

Option 3: 30°

Option 4: 60“

Question : A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°. Then the distance of the person from the pole is:

Option 1: $5\sqrt3$ metres

Option 2: $\frac{5}{\sqrt3}$ metres

Option 3: $\sqrt3$ metres

Option 4: $10\sqrt3$ metres

Question : If the radius of the base, and the height of a right circular cone are increased by 20%, what is the approximate percentage increase in volume?

Option 1: 60

Option 2: 68.8

Option 3: 72.8

Option 4: 75