From a point A on the ground, the angle of elevation of the top of a 20 m tall building is \[45{}^\circ .\]A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is \[60{}^\circ .\]Find the length of flag staff. |
A) 15.23 m
B) 14.64 m
C) 14 m
D) 15.65 m
Correct Answer: B
Solution :
Given, BC = 20 m |
\[\angle BAC=45{}^\circ \] |
and \[\angle DAC=60{}^\circ \] |
In \[\Delta BAC,\]\[\tan 45{}^\circ =\frac{BC}{AC}\] |
\[\Rightarrow \] \[AC=20\,\,m\] |
In \[\Delta DAC,\] |
\[\tan 60{}^\circ =\frac{DC}{AC}=\frac{x+20}{20}\]\[\Rightarrow \]\[\sqrt{3}=\frac{x+20}{20}\] |
\[\Rightarrow \] \[x=20\sqrt{3}-20\] |
\[=34.64-20=14.64\,\,m\] |
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