If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its … cloud is h(tan β +…
Answers:
Let AN be the surface of the lake and O be the point of observation such that OA = h metres.
Let P be the position of the cloud and P’ be its reflection in the lake
Then PN = P’N
Let OM ⊥ PN
Also, ∠POM = α and ∠P’OM = β
Let PM = x
Then PN = PM + MN = PM + OA = x + h
In rt. ΔOPM, we have
In rt. ΔOMP’, we have,
Equating (1) and (2):
Hence, height of the cloud is given by PN = x + h
Hence proved.
tan Alpha=H-h/x
X=H-h/tan alfa
tan beta =H+h/x
Tan beta =H+h/H-h/tan alfa
Tan beta=tan alfa (H+h)/H-h
Tan beta (H-h)=Htan alfa + htan alfa
Htan beta -Htan alfa=htan alfa + htan beta
H(tan beta -tan alfa ) = h(tan alfa+tan beta )
H=h(tan alfa+tan beta)/tan beta-tan alfa