Question

The height of two poles are x and y meter respectively. If the poles are a meter apart then the point of intersection of the lines joining the top of each pole from opposite foot of the pole is given by.


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Answer 1

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Let AB and CD be two poles of heights a metres and b metres respectively such that the poles are p metres apart i.e.AC=p metres. Suppose the lines AD and BC meet at O such that OL=h metres. 

Let CL=x and LA=y. Then, x+y=p.

In △ABC and △LOC, we have

     ∠CAB=∠CLO           [Each equal to 90∘]

     ∠C=∠C                    [Common]

∴ △CAB∼△CLO           [By AA-criterion of similarity]

⇒ CLCA=LOAB

⇒ xp=ha

⇒ x=aph

In △ALO and △ACD, we have

   ∠ALO=∠ACD            [Each equal to 90∘]

  ∠A=∠A                    [Common] 

∴ △ALO∼△ACD      [By AA-criterion of similarity]     

⇒ ACAL=DCOL

⇒ py=b

Answer 2

Answer:

Refer to attachment..