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PQ is a post of given height ‘a’, and AB is a tower at some distance. If $α$ and $β$ are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.

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h = a tan α

h = a tan α (tan α − tan β)

h = tan α (tan α − tan β)

h = 1 (tan α − tan β)

answer is B.

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Detailed Solution

Suppose if P is the bottom of the post and Q is the top of the post, then it is given that the top of the tower is denoted by B and bottom as A. Let the diagram be,
Question Image

In right-angled triangle PAB,

tan α = A B A P tan α = h d

h = d tan α

… (1)
In right-angled triangle BQM,

tan β = B M Q M tan β = h − a d h − a = d tan β

h = a + d tan β

… (2)
From (1) and (2), and we have

d tan α = a + d tan β d (tan α − tan β) = a d = a tan α − tan β

Substitute the above value in (1), and we have

h = d tan α h = a tan α (tan α − tan β)

Hence, the correct option is 2.

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