Let a vertical tower AB have its end A on the level ground

Let a vertical tower AB have its end A on the level ground. Let C be the midpoint of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to:

  1. 6/7
  2. 1/4
  3. 2/9
  4. 4/9

Solution

tan (θ + β) = 1/2

and tan θ = 1/4

\( \frac{1/4 + \tan\beta}{1 - 1/4 \tan\beta} = \frac{1}{2} \)

9 tanβ = 2

tan β = 2/9

The correct option is C.