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Question: The angle of elevation of a cliff at a point A on the ground and a point B, 100 m vertically at A ar...

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

A

100cot⁡αcot⁡α−cot⁡β\frac { 100 \cot \alpha } { \cot \alpha - \cot \beta }

B

100cot⁡βcot⁡α−cot⁡β\frac { 100 \cot \beta } { \cot \alpha - \cot \beta }

C

100cot⁡βcot⁡β−cot⁡α\frac { 100 \cot \beta } { \cot \beta - \cot \alpha }

D

100cot⁡βcot⁡β+cot⁡α\frac { 100 \cot \beta } { \cot \beta + \cot \alpha }

Answer

100cot⁡βcot⁡β−cot⁡α\frac { 100 \cot \beta } { \cot \beta - \cot \alpha }

Explanation

Solution

If OP=hO P = h then CP=h−100C P = h - 100Now, equate the values of OA and BC

hcot⁡α=(h−100)cot⁡βh \cot \alpha = ( h - 100 ) \cot \beta

∴\therefore h=100cot⁡βcot⁡β−cot⁡αh = \frac { 100 \cot \beta } { \cot \beta - \cot \alpha }