Question

Two post are K metre apart and height of one is double that of other . if from the midpoint of the line segment joining their feet an observer Finds the angle of elevation of their tops to be complementary then find the height of shortest post

Answer 1

Answer:

Height of shortest post is

$\frac{k}{2\sqrt{2}}$

Step-by-step explanation:

Let AB and CD be two posts with AB=2CD

Let O be the point of observation.

As per given data,

$\theta\:and\:\:90-\theta\:$are angle elevation of top of the posts

In ΔABO

$tan\theta=\frac{AB}{OB}$.....(1)

In ΔCDO,

$cot(90-\theta)=\frac{OD}{CD}$

$tan\theta=\frac{OD}{CD}$.....(2)

From (1) and (2)

$\frac{AB}{OB}=\frac{OD}{CD}$

(AB)(CD) = (OB)(OD)

(2CD)(CD)=(OB)(OD)

$But\:OB=OD=\frac{k}{2}$

$2\:CD^2=\frac{k}{2}.\frac{k}{2}$

$2\:CD^2=\frac{k^2}{4}$

$CD^2=\frac{k^2}{4*2}$

$CD=\frac{k}{2\sqrt{2}}$

Therefore

Height of shortest post is

$\frac{k}{2\sqrt{2}}$

Answer 2

Step-by-step explanation:

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