A) \[\frac{a\sin (\alpha +\beta )}{\sin (\beta -\alpha )}m\]
B) \[\frac{a\sin (\alpha +\beta )}{\sin (\alpha -\beta )}m\]
C) \[\frac{a\sin (\beta -\alpha )}{\sin (\alpha +\beta )}m\]
D) None of these
Correct Answer: A
Solution :
In\[\Delta CDE\], \[\cot \alpha =\frac{DC}{H-a}\] ... (i) And in\[\Delta CDF\] \[\cot \beta =\frac{DC}{H+a}\] ... (ii) From Eqs. (i) and (ii), we get \[(H+a)\cot \beta =(H-a)\cot \alpha \] \[\Rightarrow \] \[H=\frac{a(-\cot \beta -\cot \alpha )}{\cot \beta -\cot \alpha }\] \[\Rightarrow \] \[H=\frac{a(\cot \alpha +\cot \beta )}{\cot \alpha -\cot \beta }\] \[=\frac{(a\cos \alpha \sin \beta +\cos \beta \sin \alpha )}{\cos \alpha \sin \beta -\cos \beta \sin \alpha }\] \[=a\frac{\sin (\alpha +\beta )}{\sin (\beta -\alpha )}m\]You need to login to perform this action.
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