Question : From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60°. If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower?

Option 1: $40 \sqrt{3}$

Option 2: $\frac{151 \sqrt{3}}{6}$

Option 3: $\frac{77}{4} \sqrt{3}$

Option 4: $\frac{40 \sqrt{3}}{3}$

Question : From the top of a cliff 100 metres high, the angles of depression of the top and bottom of a tower are 45° and 60°, respectively. The height of the tower is:

Option 1: $\frac{100}{3}(3-\sqrt{3})$ m

Option 2: $\frac{100}{3}(\sqrt3-1)$ m

Option 3: $\frac{100}{3}(2\sqrt3-1)$ m

Option 4: $\frac{100}{3}(\sqrt3-\sqrt{2})$ m

Question : From the top of a 20 metres high building, the angle of elevation from the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is: $(\sqrt{3} = 1.732)$

Option 1: 45.46 metres

Option 2: 45.64 metres

Option 3: 54.64 metres

Option 4: 54.46 metres

Question : The angle of elevation of the top of a tower from the top of a building whose height is 680 m is $45^{\circ}$ and the angle of elevation of the top of the same tower from the foot of the same building is $60^{\circ}$. What is the height (in m) of the tower?

Option 1: $340(3 + \sqrt3)$

Option 2: $310(3 - \sqrt3)$

Option 3: $310(3 + \sqrt3)$

Option 4: $340(3 - \sqrt3)$

Question : On the ground, there is a vertical tower with a flagpole on its top. At a point 9 metres away from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30°, respectively. The height of the flagpole is:

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

Option 2: $6\sqrt{3}$ metres

Option 3: $6\sqrt{2}$ metres

Option 4: $6\sqrt{5}$ metres