A) 34.64 m
B) 51.96 m
C) 69.28 m
D) 103.92 m
Correct Answer: D
Solution :
[d] \[AB=h\](Let) then, \[DC=3h\] Since, angles of elevation of both pillars from tops are complementary. \[\therefore \] \[\theta =30{}^\circ \] Now, in right angled \[\Delta ABCtan\theta =\frac{{}}{{}}\tan 30{}^\circ =\frac{h}{120}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{h}{120}\]\[\Rightarrow \]\[h=\frac{120}{\sqrt{3}}\] \[\Rightarrow \] \[h=\frac{120\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\]\[\Rightarrow \]\[h=40\sqrt{3}\] Height of big pillar \[=\frac{3h}{2}=\frac{3\times 40\sqrt{3}}{2}=60\sqrt{3}\,m\] \[=60\times 1.732=103.92\,m\] |
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