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 : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?

Option 1: $48 \sqrt{3}$

Option 2: $36$

Option 3: $36 \sqrt{3}$

Option 4: $48$

Question : A 22 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground?

Option 1: $\frac{22 \sqrt{2}}{3}$

Option 2: $11 \sqrt{2}$

Option 3: $11$

Option 4: $11 \sqrt{3}$

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