the angle of elevation of the top of a cloud as observed from a 16 tall building is 60 degree and the angle of depression of a foot of a hill is 30 degree find the height of the cloud
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द हाइट ऑफ द क्लाउड 30 डिग्री
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The angle of elevation of top of the cloud as observed from a 16m tall building is 60 degree. the angle of depression of foot of the hill is 30 degree.
The height of the cloud is 64m
Stepwise expleation is given below:
- As, AB is bilding
E is foot of the hill
- AE is the distance between the building and the hill
- CE is the height of the cloud from the hill
It is given that AB=16m
- So, in ΔAEB
Angle ABE is 60°
tan60°=EA/AB
√3=EA/16
16√3=EA
AE=BD=16√3
- Now, in ΔBCD
Angle CBD is 60°
tan60°=CD/BD
√3=CD/16√3
(16√3)(√3)=CD
CD=48m
AB=ED=16m
CD+ED=48+16=64m
- So the height of the cloud is 64m.
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