A) \[\frac{h\tan \beta }{\tan \alpha -\tan \beta }\]
B) \[\frac{h\tan \alpha }{\tan \alpha +\tan \beta }\]
C) \[\frac{h\tan \beta }{\tan \alpha +\tan \beta }\]
D) \[\frac{h\tan \alpha }{\tan \beta -\tan \alpha }\]
Correct Answer: D
Solution :
\[\therefore \] Height of the light house = 225 m |
Let BC be the tower, CD the flagstaff and |
\[\angle BAC=\alpha \]and \[\angle BAD=\beta \] |
In \[\Delta ABC,\] |
\[\tan \alpha =\frac{BC}{AC}\] ?(i) |
and in \[\Delta ABD,\] |
\[\frac{BD}{AC}=\frac{BC+h}{AC}=\tan \beta \] ?(ii) |
On dividing Eq. (ii) by Eq. (i), we get |
\[\frac{BC+h}{BC}=\frac{\tan \beta }{\tan \alpha }\] |
\[\Rightarrow \] \[(BC+h)\tan \alpha =BC=\tan \beta \] |
\[\Rightarrow \] \[BC\,\,(\tan \beta -\tan \alpha )=h\tan \alpha \] |
\[\Rightarrow \] \[BC=\frac{h-\tan \alpha }{\tan \beta -\tan \alpha }\] |
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