Question

If the angle of elevation of the top of a tower $100mt$ from a point to its foot is ${\tan }^{-1}\left(\frac{4}{5}\right)$ then the distance from the point to its foot is

• A. $125m$
• B. $150m$
• C. $200m$
• D. $360m$

Answer 1

The correct option is A $125m$

Let $QR$ be the tower.

Given, height=$100m$

Let $\alpha$ be the angle of elevation.
$\alpha ={\tan }^{-1}\left(\frac{4}{5}\right)$

In$△PQR$,

$\tan \alpha =\frac{QR}{RP}$

$\tan \left(ta{n}^{-1}\right(\frac{4}{5}\left)\right)=\frac{100}{RP}$

$⟹\frac{4}{5}=\frac{100}{RP}$

$⟹RP=\frac{5\times 100}{4}=125m$

Hence the distance from point to it's foot is $125m$.