question_answer

From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 12 m and 27 m the two points lie on the same side of the pillar, then the height of the pillar is

[SSC (CPO) 2015]

A) 15 m                

B) 12 m

C) 16 m                            

D) 18 m

Correct Answer: D

Solution :

In \[\Delta ABC,\] \[\tan \theta =\frac{h}{12}\]                  ..(i)

Now in \[\Delta ABD,\]

\[\tan (90{}^\circ -\theta )=\frac{h}{27}\]

\[\Rightarrow \]   \[\cot \theta =\frac{h}{27}\]                    (ii)

On multiplying Eqs. (i) and (ii), we get

\[\tan \theta \cdot \cot \theta =\frac{h}{12}\times \frac{h}{27}\]

\[\Rightarrow \]   \[1-\frac{{{h}^{2}}}{324}\]\[\Rightarrow \]\[{{h}^{2}}=324\]\[\Rightarrow \]\[h=18\]

Hence, height of pillar is 18 m.