Two poles, AB of length a metres and CD of length a + b (b [] a) metres are erected at the…

Question

Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan$$\angle$$ACB = $${1 \over 2}$$, then :

Accepted Answer

$$\tan \theta  = {1 \over 2}$$

$$\tan (\theta  + \alpha ) = {x \over b},\tan \alpha  = {x \over {a + b}}$$

$$ \Rightarrow {{{1 \over 2} + {x \over {a + b}}} \over {1 - {1 \over 2} \times {x \over {a + b}}}} = {x \over b}$$

$$ \Rightarrow {x^2} - 2ax + ab + {b^2} = 0$$

Solutions · 1