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 \[\Delta DBC,\]\[\tan 45{}^\circ =\frac{DB}{BC}\] |
\[\Rightarrow \] \[1=\frac{AD+AB}{BC}\] |
\[\Rightarrow \] \[BC=AD+86.5\] |
\[150-86.6=AD\] |
\[\Rightarrow \] \[AD=63.4\,\,m\] |
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