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 \[\angle CAD\] |
\[\tan 60{}^\circ =\frac{AC}{AD}=\frac{AB+BC}{AD}\] |
\[\sqrt{3}=\frac{10+BC}{10\sqrt{3}}\] |
\[\sqrt{3}\times 10\sqrt{3}=10+BC\] |
\[\Rightarrow \]\[10\times 3=10+BC\]\[\Rightarrow \]\[BC=20\,\,m\] |
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