Question

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

पर्याय

• True

• False

Answer 1

This statement is False.

Explanation:

Case I: Let the height of the tower is h and BC = x m

In ΔABC,

tan 30° = `"AC"/"BC" = "h"/x`

⇒ `1/sqrt(3) = "h"/x`  ...(i)

Case II: By condition, the height of the tower is doubled i.e., PR = 2h.

 In ΔPQR,

tan θ = `"PR"/"QR" = (2"h")/x`

⇒ tan θ = `2/x xx x/sqrt(3)`  ...`[∵ "h" = x/sqrt(3), "from equation (i)"]`

⇒ tan θ = `2/sqrt(3)` = 1.15

∴ θ = tan^–1(1.15) < 60°

Hence, the required angle is not doubled.