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 unchanged.

पर्याय

• True

• False

Answer 1

This statement is True.

Explanation:

Case (i): Let the height of a tower be h and the distance of the point of observation from its foot is x.

In ∆ABC,

tan θ₁ = `"AC"/"BC" = "h"/x`  ...(i)

Case (ii): Now, the height of a tower increased by 10%

= h + 10% of h

= `"h" + "h" * 10/100`

= `(11"h")/100`

And the distance of the point of observation from its foot

= x + 10% of x

= `x + x xx 10/100 = (11x)/10`

In ΔPQR,

tan θ₂ = `"PR"/"QR" = (((11"h")/10))/(((11x)/10))`

⇒ tan θ₂ = `"h"/x`  ...(ii)

From equations (i) and (ii), we get

tan θ₁ = tan θ₂ 

⇒ θ₁ = θ₂

Hence, the required angle of elevation of its top remains unchanged.