question_answer

The angle of elevation of a cliff at a point A on the ground and a point B, 100 m vertically at A are a and b respectively. The height of the cliff is [EAMCET 1986]

A) \[\frac{100\,\,\cot \,\alpha }{\cot \alpha -\cot \beta }\]

B) \[\frac{100\,\,\cot \beta }{\cot \,\alpha -\cot \,\beta }\]

C) \[\frac{100\,\,\cot \beta }{\cot \beta -\cot \alpha }\]

D) \[\frac{100\,\,\cot \beta }{\cot \beta +\cot \alpha }\]

Correct Answer: C

Solution :

If\[OP=h\], then \[CP=h-100\] Now equate the values of \[OA\] and\[BC\]. \[h\cot \alpha =(h-100)\,\cot \beta \] \[\therefore \] \[h=\frac{100\cot \beta }{\cot \beta -\cot \alpha }\]