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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.
Options
True
False
Solution
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.
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