Question

If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains ______.

Answer 1

If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains same.

Explanation:

Let the tower height = h and observation distance = x, so `tan θ = h/x`.

Increasing both by 10% gives new height `((11h)/10)` and new distance `((11x)/10)`.

So new tangent = `((11h)/10)/((11x)/10)`

= `h/x`

= tan θ 

Hence the angle of elevation is same.