Question : Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between the two ships is: (take $\sqrt{3}= 1.73$)

Option 1: 173 metres

Option 2: 200 metres

Option 3: 273 metres

Option 4: 300 metres

Question : The angle of depression of two ships from the top of a lighthouse is $60^{\circ}$ and $45^{\circ}$ towards the east. If the ships are 300 metres apart, the height of the lighthouse (in metres) is:

Option 1: $200\left ( 3+\sqrt{3} \right )$

Option 2: $250\left ( 3+{\sqrt3} \right )$

Option 3: $150\left (3 +{\sqrt3} \right)$

Option 4: $160 \left (3+{\sqrt3} \right)$

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

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 : A Navy captain is going away from a lighthouse at the speed of $4(\sqrt3–1)$ m/s. He observed that it took him 1 minute to change the angle of elevation of the top of the lighthouse from 60° to 45°. What is the height (in meters) of the lighthouse?

Option 1: $240\sqrt{3}$

Option 2: $480(\sqrt{3}–1)$

Option 3: $360\sqrt{3}$

Option 4: $280\sqrt{2}$