Question

From a point 10 m above the ground , the angle of elevation of the top of a tower is α and the angle of depression is β . If tan α = `5/2` and tan β = `1/4` , calculate the height of the tower to the nearest metre .

Answer 1

Let AD be the tower and B be the point of observation.

In ΔABC,

tan ∝ = `"AC"/"BC"`

⇒ `"h"/"x" = 5/2`  ....(1)

In ΔBED,

`tanβ = "BE"/"ED"`

⇒ `1/4 = 10/"x"`

⇒ x = 40

From (1),
h = 100

∴ Height of the tower = h + 10 = 100 + 10 = 110 m