if the angle of elevation of a cloud from a point h metres above a lake is alpha and the angle of depression of tits reflection in the lake be beta, prove that distance of the cloud from the point of observation is 2h sec alpha/tan beta - tan alpha
Answers
Distance of the cloud from the point of observation = 2hSecα/(Tanβ - Tanα)
Step-by-step explanation:
Let sat Height of Cloud from point of observation = C
Height of cloud from Lake = C + h
Depth of Cloud reflection from point of observation = C + h + h = C + 2h
Horizontal Distance of cloud from point of observation = B
Tanα = C/B
=> C = BTanα
Tanβ = (C + 2 h)/B
=> C = BTanβ - 2 h
BTanα = BTanβ - 2 h
=> 2h = BTanβ - BTanα
=> 2h = B(Tanβ - Tanα)
=> B = 2h/(Tanβ - Tanα)
Cosα = B/distance of the cloud from the point of observation
=> distance of the cloud from the point of observation = B/Cosα
= BSecα
= 2hSecα/(Tanβ - Tanα)
distance of the cloud from the point of observation = 2hSecα/(Tanβ - Tanα)
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