Question : Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 metres, the distance between the two men is: (take $\sqrt{3}=1.732$)

Option 1: $136.6$ metres

Option 2: $50\sqrt{3}$ metres

Option 3: $100\sqrt{3}$ metres

Option 4: $135.5$ metres

Question : From the top of a building 60 metres high, the angles of depression of the top and bottom of a tower are observed to be $30^{\circ}$ and $60^{\circ}$, respectively. The height of the tower in metres is:

Option 1: 40

Option 2: 45

Option 3: 50

Option 4: 55

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 : A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retreats 36 m from the bank, he finds that the angle is 30°. The breadth of the river is:

Option 1: 15 metres

Option 2: 18 metres

Option 3: 16 metres

Option 4: 11 metres

Question : A helicopter, at an altitude of 1500 metres, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are $60^{\circ}$ and $30^{\circ}$, respectively. Distance between the two ships, in metres, is:

Option 1: $1000\sqrt{3}$

Option 2: $\frac{1000}{{\sqrt3}}$

Option 3: $500{\sqrt3}$

Option 4: $\frac{500}{{\sqrt3}}$