Question

If two towers of heights h₁ and h₂ subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h₁: h₂ = ____________.

Options

• 1 : 2

• 1 : 3

• 2 : 1

• 3 : 1

Answer 1

If two towers of heights h₁ and h₂ subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h₁: h₂ = 3 : 1.

Explanation:

`"h"_1 = "tan"  60^circ = sqrt3`

`=> "h"_1 = sqrt3  "x"`

`"h"_2/"x" = "tan"  30^circ = 1/sqrt3`

`=> "h"_2 = 1/sqrt3 "x"`

`"h"_1/"h"_2 = (sqrt 3  "x")/(1/sqrt3  "x") = 3/1`

`=> "h"_1 : "h"_2 = 3 : 1`