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Height and Distance
Height and Distance
Easy

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∠\angleACB = 12{1 \over 2}, then :

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Solution

tan⁡θ=12\tan \theta = {1 \over 2} tan⁡(θ+α)=xb,tan⁡α=xa+b\tan (\theta + \alpha ) = {x \over b},\tan \alpha = {x \over {a + b}} ⇒12+xa+b1−12×xa+b=xb \Rightarrow {{{1 \over 2} + {x \over {a + b}}} \over {1 - {1 \over 2} \times {x \over {a + b}}}} = {x \over b} ⇒x2−2ax+ab+b2=0 \Rightarrow {x^2} - 2ax + ab + {b^2} = 0

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