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Question 11
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 the doubled.


Solution

The statement is false.
Case I:
Let the height of the tower is h and BC = x m.

tan 30=ACBC=hx

13=hx(i)



Case II 

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

In
ΔPQR,tan θ=PRQR=2hx

tan θ=2x×x3   [h=x3fromEq.(i)]

tan θ=23=1.15

θ=tan1(1.15)<60

Hence, the required angle is not doubled.
                                            

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