question_answer

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 \[\Delta DAC,\]

\[\tan 60{}^\circ =\frac{DC}{AC}=\frac{x+20}{20}\]\[\Rightarrow \]\[\sqrt{3}=\frac{x+20}{20}\]

\[\Rightarrow \]   \[x=20\sqrt{3}-20\]

\[=34.64-20=14.64\,\,m\]