CBSE Class 10 Answered
From the top of the tower the angles of depression of 2 objects on the same side of the tower are found to be alpha and beta(alpha greater than beta).If the distance between the objects is (p)m . show that the height of the tower is
h=ptan alpha tan beta divided by tan alpha -tan beta.also determine the height of the tower.if p=50m,alpha=60 degrees and beta= 30 degrees
Asked by Harshita Bhola | 23 Nov, 2010, 12:00: AM
Expert Answer
Dear student,
DC = p
and AB = h
Let BC = x
Then in triangle ABD
tanα = h/(x-p)………………………………..(1)
and in triangle ABC
tanβ = h/x……………………………………..(2)
Eliminating x from equations (1) and (2)
=> tanα = h/(h/tanβ - p)
=> h tanα/ tanβ - p tanα = h
=> h = p tanα tanβ /( tanα - tanβ)
Hence Proved.
Substituting p = 50, α = 600 and β = 300
h = 43.3 metres.
Regards Topperlearning.
Answered by | 26 Nov, 2010, 11:36: PM
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