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

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

Answer 1

The correct option is B $\frac{h\cot p}{\cot p-\cot q}$

From $△ABE$
$\frac{BE}{AB}=\tan q\Rightarrow AB=(h+x)\cot q...\left(1\right)$
From $△CDE$
$\frac{DE}{CD}=\tan p\Rightarrow CD=x\cot p...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\Rightarrow (x+h)\cot q=x\cot p$
$\Rightarrow x=\frac{h\cot q}{\cot p-\cot q}$
$\Rightarrow x+h=\frac{h\cot p}{\cot p-\cot q}$
$\therefore BE=\frac{h\cot p}{\cot p-\cot q}$