A) 50 m
B) \[50\sqrt{3}m\]
C) \[50(\sqrt{3}-1)m\]
D) \[50\left( 1-\frac{\sqrt{3}}{3} \right)m\]
Correct Answer: D
Solution :
[d] Let height of the tower be h m and distance between tower and cliff be x m. |
\[\therefore \,\,\,CD=h,\,\,\,BD=x\] |
In \[\Delta ABD,\,\,\,\tan 45{}^\circ =\frac{AB}{BD}\] |
or \[1=\frac{50}{x}\] |
\[x=50\] ? (i) |
In \[\Delta AEC\] |
\[tan\,\,30{}^\circ =\frac{AE}{EC}=\frac{AB-EB}{EC}=\frac{AB-DC}{BD}\] |
\[(\because \,\,\,\,EB=DC,\,\,EC=BD)\] |
\[\frac{1}{\sqrt{3}}=\frac{50-h}{x}\] or \[x=50\sqrt{3}-h\sqrt{3}\] |
or \[50=50\sqrt{3}-h\sqrt{3}\] or \[h\sqrt{3}=50\sqrt{3}-50\] |
or \[h=\frac{50(\sqrt{3}-1)}{\sqrt{3}}=50\left( 1-\frac{1}{\sqrt{3}} \right)\] |
\[\therefore \,\,\,\,\,h=50\left( 1-\frac{\sqrt{3}}{3} \right)\] |
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