question_answer

The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is \[30{}^\circ .\]If the angle of elevation at the same point is to be \[45{}^\circ ,\]then the pillar has to be raised to a height of how many metres?

A) 59.4 m             

B) 61.4 m

C) 62.4 m             

D) 63.4 m

Correct Answer: D

Solution :

Given, \[BC=150\,\,m\]

\[\angle ACB=30{}^\circ \]and \[\angle DCB=45{}^\circ \]

Then,    \[AD=?\]

In \[\Delta ABC,\]\[\tan 30{}^\circ =\frac{AB}{BC}\]\[\Rightarrow \]\[\frac{1}{\sqrt{3}}=\frac{AB}{150}\]

\[\therefore \]                  \[AB=86.6\,\,m\]

In \[\Delta DBC,\]\[\tan 45{}^\circ =\frac{DB}{BC}\]

\[\Rightarrow \]               \[1=\frac{AD+AB}{BC}\]

\[\Rightarrow \]               \[BC=AD+86.5\]

\[150-86.6=AD\]

\[\Rightarrow \]               \[AD=63.4\,\,m\]