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 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 : The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds of flight, the elevation changes to 30°. If the aeroplane is flying at a height of $1500\sqrt{3}$ metre, find the speed of the plane:

Option 1: 300 m/sec

Option 2: 200 m/sec

Option 3: 100 m/sec

Option 4: 150 m/sec

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 : The angle of elevation of a ladder leaning against a house is 60°, and the foot of the ladder is 6.5 metres from the house. The length of the ladder is:

Option 1: $\frac{13}{\sqrt{3}}$ metres

Option 2: $13$ metres

Option 3: $15$ metres

Option 4: $3.25$ metres