Question

If the angle of elevation of a cloud from a point of h meters above a lake is A and the angle of depression of its reflection in the lake is B prove that the height of the cloud is h(tan B+tan A/tan B-tan A)

Answer 1

Answer:

In right ∆ABC,

tanA = x/AB

AB = x/tanA___________(i)

In right ∆ABD,

tanB = BD/AB

tanB = h+x+h /AB

AB = 2h+x/tanB_________(ii)

From equation (i) & (ii),

x/tanA = 2h+x/tanB

xtanB = 2h*xtanA+xtanA

xtanB — xtanA = 2htanA

x(tanB-tanA) = 2htanA

x= 2htanA/tanB—tanA

Height of cloud = x+h = 2htanA/tanB—tanA + h

2htanA+h(tanB—tanA)/tanB—tanA

htanA+htanB/tanB—tanA

h(tanA+tanB)/tanB-tanA,

Hence, Proved.

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Answer 2

Step-by-step explanation:

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