Question

The top of a hill observed from the top and bottom of a building of height ${}^{\prime }{h}^{\prime }$ is at angles of elevation $p$ and $q$, respectively. The height of hill is ?

• A. $\frac{h\cot q}{\cot q-\cot q}$
• B. $\frac{h\cot p}{\cot p-\cot q}$
• C. $\frac{h\tan p}{\tan p-\tan q}$
• D. None of these

Answer 1

Answer: (B)

$\frac{h\cot p}{\cot p-\cot q}$

Let $AD=h$ is the height of the building and $EB$ is height of the hill.
and $\tan q=\frac{h+x}{y}$
and $\tan p=\frac{x}{y}$
$\Rightarrow y=x\cot p$
Now, $\tan q=\frac{h+x}{x\cot p}$
$\Rightarrow x\cot p=(h+x)\cot q$
$\Rightarrow x=\frac{h\cot q}{\cot p-\cot q}$
$\therefore h+x=h+\frac{h\cot q}{\cot p-\cot q}$
$=\frac{h\cot p}{\cot p-\cot q}$