Question : The cliff of a mountain is 180 m high and the angles of depression of two ships on either side of the cliff are 30° and 60°. What is the distance between the two ships?

Option 1: $400$ metres

Option 2: $400\sqrt{3}$ metres

Option 3: $415.68$ metres

Option 4: $398.6$ 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 : The two banks of a canal are straight and parallel. A, B, and C are three persons, of whom A stands on one bank and B and C on the opposite banks. B finds the angle ABC is 30°, while C finds that the angle ACB is 60°. If B and C are 100 metres apart, the breadth of the canal is:

Option 1: $\frac{25}{\sqrt{3}}$ metres

Option 2: $20\sqrt{3}$ metres

Option 3: $25\sqrt{3}$ metres

Option 4: $\frac{20}{\sqrt{3}}$ metres

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: $\sqrt{3}$