A) \[45{}^\circ \]
B) \[60{}^\circ \]
C) \[30{}^\circ \]
D) \[90{}^\circ \]
Correct Answer: B
Solution :
Let OA and AB be the shadows of tower OR and flagstaff RC respectively on the grounds. |
Let the sun makes an angle \[\phi \]with the ground. |
Let \[OA=x\] |
In right angled \[\Delta OAR,\] |
\[\tan \phi =\frac{h}{x}\] ?(i) |
and in \[\Delta OBQ,\]\[\tan \phi =\frac{h+6}{x+2\sqrt{3}}\] ?(ii) |
From Eqs. (i) and (ii), |
\[\therefore \] \[\frac{h}{x}=\frac{h+6}{x+2\sqrt{3}}\] |
\[h\,\,(x+2\sqrt{3})=x\,\,(h+6)\] |
\[2\sqrt{3}h=6x\] |
\[x=\frac{h}{\sqrt{3}}\]\[\Rightarrow \]\[\frac{h}{x}=\sqrt{3}\] |
\[\Rightarrow \] \[\tan \phi =\sqrt{3}\] [from Eq. (i)] |
\[\Rightarrow \] \[\phi =60{}^\circ \] |
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