The angle of elevation of an aeroplane from a point A on the ground is 60° . After a flight of 15 seconds, the angle of elevation changed to 30° . If the aeroplane is flying at a constant height of 1500 √3 m, find the speed of the plane in km/hr. OR At a point A, 20 metre above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60° . Find the distance of the cloud from A ?
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Answer:
Height of aeroplane =BD=CE=1500
3
m and
∠BAE=60
0
and CAE=30
0
In triangle ADB
tan60
0
=
AD
1500
3
⇒
3
=
AD
1500
3
⇒AD=1500 m
In triangle CAE
tan30
0
=
AE
1500
3
⇒
3
1
=
AD
1500
3
⇒AE=1500×3=4500 m
Distance covered by plane in 15 seconds: BC=DE=AE−AD=4500−1500=3000 m
Speed of aeroplane =
15
3000
=200 m/s=720 km/hr
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