question_answer

There is a flag staff on top of a building. The height of the building being 10 m. At a point certain distance away from the foot of the building the angles of elevation to the top and bottom of flag staff are \[60{}^\circ \] and \[30{}^\circ ,\]respectively. Find the height of the flag staff.

A) 20 m                

B) 5 m

C) 15 m                

D) 25 m

Correct Answer: A

Solution :

(a)

Let AB be the height of the building and BC the height of the flag staff.

Then, \[AB=10\,\,m,\]

\[\angle ADB=30{}^\circ ,\]\[\angle ADC=60{}^\circ \]

In right angled \[\Delta BAD,\]\[\tan 30{}^\circ =\frac{AB}{AD}\]

\[\Rightarrow \]   \[\frac{1}{\sqrt{3}}=\frac{10}{AD}\]

In right angled \[\angle CAD\]

\[\tan 60{}^\circ =\frac{AC}{AD}=\frac{AB+BC}{AD}\]

\[\sqrt{3}=\frac{10+BC}{10\sqrt{3}}\]

\[\sqrt{3}\times 10\sqrt{3}=10+BC\]

\[\Rightarrow \]\[10\times 3=10+BC\]\[\Rightarrow \]\[BC=20\,\,m\]