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

Step-by-step solution

Let ∠ A P C = α Given, A B = 2 A C = 2 B C Also A P = 2 A B ⇒ A P = 4 A C = 4 B C ⇒ tan α = A C A P = A C 4 A C = 1 4 ⇒ tan α + β = A B A P = A B 2 A B = 1 2 Let, tan β = x tan α + tan β 1 - tan α   ⋅ tan β = 1 2 ⇒   1 4 + x 1 - x 4 = 1 2 ⇒   1 + 4 x 4 - x = 1 2 ⇒     2 + 8 x - 4 + x = 0 ⇒     9 x - 2 = 0 ⇒     x = 2 9