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The angle of elevation theta of the top ...

The angle of elevation `theta` of the top of a tower is `30^(@)`. If the height of the tower is doubled, then new `tan theta` will be

A

`sqrt 3/2`

B

`3/2`

C

`2/3`

D

`2/sqrt 3`

Text Solution

Verified by Experts

The correct Answer is:
D
False,
Case I Let the height of the tower is h and BC = xm
In `DeltaABC`,
`tan30^(@)=(AC)/(BC) = h/x`
`rArr 1/sqrt(3) = h/x`………(i)
Case II By condition, the height of the tower is doubled, i.e., PR=2h.
In `DeltaPQR`, `tantheta=(PR)/(QR)=(2h)/x`
`rArr tantheta=2/x xx x/sqrt(3)` `[therefore h=x/sqrt(3)]`, from Eq. (i)
`rArr tantheta=2/sqrt(3) = 11.5`
`therefore theta=tan^(-1)(1.15) lt 60^(@)` M
Hence, the requried angle is not doubled.
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