A) \[\frac{h(1+\tan \theta )}{(1-\tan \theta )}\]
B) \[\frac{h(1-\tan \theta )}{1+\tan \theta }\]
C) \[h\,\tan \,({{45}^{o}}-\theta )\]
D) None of these
Correct Answer: A
Solution :
Let A be position of cloud and height of cloud be H metres. In \[\Delta \,ABC,\,\cot \theta =\frac{BC}{H-h}\] \[(H-h)\,cot\theta =BC\] ?..(i) Also, in \[\Delta BCD,\,\,\cot {{45}^{p}}=\frac{BC}{H+h}\] \[\Rightarrow \] \[BC=(H+h)\,\,\cot {{45}^{o}}\] ...(ii) From (i) and (ii), we get \[(H-h)\,\cot \theta =(H+h)cot{{45}^{o}}\] \[\Rightarrow \] \[\frac{H+h}{H-h}=\frac{\tan {{45}^{o}}}{\tan \theta }\] Applying componendo and dividendo, we get (ii) \[\Rightarrow \] \[\frac{H+h+H-h}{H+h-H+h}=\frac{\tan {{45}^{o}}+\tan \theta }{\tan {{45}^{o}}-\tan \theta }\] \[\Rightarrow \] \[H=h\left( \frac{1+\tan \theta }{1-\tan \theta } \right)\]You need to login to perform this action.
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