Question : The length of the shadow of a vertical tower on level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. The height of the tower is:

Option 1: $10 \sqrt{3}$ m

Option 2: $5 \sqrt{3}$ m

Option 3: $5(\sqrt{3}+1)$ m

Option 4: $10(\sqrt{3}+1)$ m

Question : The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it was 60°. The height of the tower is:

Option 1: $5\sqrt{3}-1$ metres

Option 2: $5(3+\sqrt{3})$ metres

Option 3: $10(\sqrt{3}-1)$ metres

Option 4: $10(\sqrt{3}+1)$ metres

Question : If the length of the shadow of a vertical pole is $\sqrt{3}$ times the height of the pole, the angle of elevation of the sun is:

Option 1: $60°$

Option 2: $45°$

Option 3: $30°$

Option 4: $90°$

Question : If the angle of elevation of the sun decreases from $45^\circ$ to $30^\circ$, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is:

Option 1: $60(\sqrt{3}+1)$ metres

Option 2: $30(\sqrt{3}–1)$ metres

Option 3: $30(\sqrt{3}+1)$ metres

Option 4: $60(\sqrt{3}–1)$ metres

Question : At 129 m away from the foot of a cliff on level ground, the angle of elevation of the top of the cliff is 30°. The height of this cliff is:

Option 1: $50\sqrt{3}$ m

Option 2: $45\sqrt{3}$ m

Option 3: $43\sqrt{3}$ m

Option 4: $47\sqrt{3}$ m

Question : The respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. What will be the angle of elevation of the top of the tower?

Option 1: 30°

Option 2: 60°

Option 3: 90°

Option 4: 45°