Question

A house of height $100$ metres subtends a right angle at the window of an opposite house. If the height of the window is $64$ metres, then the distance between the two houses is

• A. $64$
• B. $48$
• C. $16$
• D. $32$

Answer 1

The correct option is B $48$

In $\Delta BCD,$
$\tan \theta =\frac{64}{x}...\left(i\right)$
In $\Delta AED,$
$\tan \theta =\frac{x}{100-64}...\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right),$
$x^2=64\times 36$
$\Rightarrow x=8\times 6=48$ m