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 : 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 : 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 : A kite is flying at a height of 50 metres. If the length of the string is 100 metres, then the inclination of the string to the horizontal ground in degree measure is:

Option 1: 90°

Option 2: 60°

Option 3: 45°

Option 4: 30°

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