A) \[\frac{d}{\sqrt{{{\cot }^{2}}\alpha +{{\cot }^{2}}\beta }}\]
B) \[\frac{d}{\sqrt{{{\tan }^{2}}\alpha -{{\tan }^{2}}\beta }}\]
C) \[\frac{d}{\sqrt{{{\tan }^{2}}\alpha +{{\tan }^{2}}\beta }}\]
D) \[\frac{d}{\sqrt{{{\cot }^{2}}\alpha -{{\cot }^{2}}\beta }}\]
Correct Answer: A
Solution :
Let h be the height of the tower. \[\therefore \]\[\ln \Delta OBT,\] \[OB=h\cot \beta \] Also, in triangle OAT, \[OA=h\cot \alpha \] \[\therefore \]\[d=\sqrt{O{{B}^{2}}+O{{A}^{2}}}\] \[\Rightarrow \]\[d=h\sqrt{{{\cot }^{2}}\beta +{{\cot }^{2}}\alpha }\] \[\Rightarrow \]\[h=\frac{d}{\sqrt{{{\cot }^{2}}\alpha +{{\cot }^{2}}\beta }}\]You need to login to perform this action.
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