Question : As observed from the top of a lighthouse, 45 m high above the sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. The distance travelled by ship during the period of observation is: (Your answer should be correct to one decimal place.)

Option 1: 32.9 m

Option 2: 33.4 m

Option 3: 36.9 m

Option 4: 24.8 m

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 person observes that the angle of elevation of the top of a pole of height 15 metres is 30°. What is the distance (in metres) of the person from the pole?

Option 1: $15$

Option 2: $15\sqrt3$

Option 3: $\frac{15}{\sqrt3}$

Option 4: $30$

Question : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?

Option 1: $48 \sqrt{3}$

Option 2: $36$

Option 3: $36 \sqrt{3}$

Option 4: $48$

Question : From the peak of a hill 300 m high, the angle of depression of two sides of a bridge lying on the ground are $45°$ and $30°$ (both ends of the bridge are on the same side of the hill). Then the length of the bridge is:

Option 1: $300(\sqrt3 - 1)$ m

Option 2: $300(\sqrt3 + 1)$ m

Option 3: $300\sqrt3$ m

Option 4: $\frac{300}{\sqrt3}$ m