Question : The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/h is:

Option 1: $600$

Option 2: $600(\sqrt{3}+1)$

Option 3: $600\sqrt{3}$

Option 4: $600(\sqrt{3}–1)$

Question : The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 metres, then what is the speed (in m/s) of an aeroplane?

Option 1: $50\sqrt3$

Option 2: $100\sqrt3$

Option 3: $200\sqrt3$

Option 4: $300\sqrt3$

Question : From 40 metres away from the foot of a tower, the angle of elevation of the top of the tower is 60°. What is the height of the tower?

Option 1: $\frac{120}{\sqrt{3}}$ m

Option 2: $\frac{60}{{\sqrt3}}$ m

Option 3: $\frac{50}{{\sqrt3}}$ m

Option 4: $\frac{130}{{\sqrt7}}$ m

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 : 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