question_answer

The distance between two pillars is 120 m. The height of one pillar is thrice the other. The angles   of elevation of their tops from the midpoint of the   line connecting their feet are complementary to each other. The height of the taller pillar is (Use\[\sqrt{3}=1.732)\][SSC CGL Tier II, 2017]

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 \[=\frac{3h}{2}=\frac{3\times 40\sqrt{3}}{2}=60\sqrt{3}\,m\] \[=60\times 1.732=103.92\,m\]