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Question

The angle of elevation of the top of a tower from the top and foot of 100m building are 30 and 45 respectively. The height of the tower is


A

50(33)m

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B

50(3+3)m

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C

503m

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D

150 m

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Solution

The correct option is B

50(3+3)m



CD = BE = 100m,
AB = H metre
AE = AB - BE = H - 100, CE = BD
In ΔACE, tan 30=AECE
13=H100x x=3(H100)....(1)In ΔABD, tan 45=ABBD 1=Hx x=H.....(2)
From (1) and (2), we have
H=3(H100)H=3H10033HH=1003H=100331H=1003(3+1)(31)(3+1)=1003(3+1)2H=503(3+1)H=50(3+3)


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