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 : A pole of length 7 m is fixed vertically on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60° and the angle of depression of the same point on the ground from the top of the tower is 45°. The height (in m) of the tower is:

Option 1: $7(2 \sqrt{3}-1)$

Option 2: $\frac{7}{2}(\sqrt{3}+2)$

Option 3: $7 \sqrt{3}$

Option 4: $\frac{7}{2}(\sqrt{3}+1)$

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 : 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 : 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