1. Tardigrade
  2. Question
  3. Mathematics
  4. An eagle is sitting at a distance of 100 metres from base of a building. It can see a sparrow sitting at the top of the building at an angle of elevation of 30 degrees. It moves towards the building and sits at a point such that now it can see the same sparrow at an angle of elevation of 45 degrees. At what distance from the base of building is the eagle sitting now ?

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Q. An eagle is sitting at a distance of $ 100 $ metres from base of a building. It can see a sparrow sitting at the top of the building at an angle of elevation of $ 30 $ degrees. It moves towards the building and sits at a point such that now it can see the same sparrow at an angle of elevation of $ 45 $ degrees. At what distance from the base of building is the eagle sitting now ?

J & K CETJ & K CET 2018

Solution:

Let $h$ be the height o f the building In $\Delta ABC$, we have
$tan\,45^{\circ} = \frac{h}{x} $
$\Rightarrow h = x \,\,\,...(i)$
image
In $ \Delta ABD$, we have
$tan\,30^{\circ} = \frac{h}{100}$
$\Rightarrow h = \frac{100}{\sqrt{3}} m$
$\therefore $ From $(i)$, we have,
$x = \frac{100}{\sqrt{3}} m = 57.735\,m$