The angle of elevation of an aeroplane from point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

Height of aeroplane=BD=CE=1500√3 m and ∠BAE=60° and ∠CAE=30°
In triangle ADB
tan60°=1500√3/AD ⇒ √3=1500√3/AD ⇒AD=1500 m
In triangle CAE
tan30°=1500√3/AE ⇒ 1/√3=1500√3/AE ⇒AE=1500×3=4500 m
Distance covered by plane in 15 seconds: BC=DE=AE−AD=4500−1500=3000 m
Speed of aeroplane=3000/15=200 m/s=720 km/hr