Question

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 ?

• A. $57.735$ metres
• B. $70.711$ metres
• C. $100$ metres
• D. $173.205$ metres

Answer 1

Answer: (A)

Let $h$ be the height o f the building In $\Delta ABC$, we have
$tan45^{\circ }=\frac{h}{x}$
$\Rightarrow h=x...(i)$

In $\Delta ABD$, we have
$tan30^{\circ }=\frac{h}{100}$
$\Rightarrow h=\frac{100}{\sqrt{3}}m$
$\therefore$ From $(i)$, we have,
$x=\frac{100}{\sqrt{3}}m=57.735m$