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 | 23rd 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  | 26th Nov, 2010, 11:36: PM

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