Question

Find $h$ if $\alpha ={60}^o,\beta ={30}^o$ and $x=400m$.

• A. $172.2m$
• B. $179.2m$
• C. $173.2m$
• D. None of these
  

Answer 1

Answer: (C)

$173.2m$

$\alpha ={60}^o$
Hence
$\cot \alpha =\frac{1}{\sqrt{3}}$
$\beta ={30}^o$
$\cot \beta =\sqrt{3}$
Hence
$h=\frac{x}{\cot \alpha +\cot \beta }$

$=\frac{400}{\sqrt{3}+\frac{1}{\sqrt{3}}}$

$=\frac{400\sqrt{3}}{3+1}$

$=\frac{400\sqrt{3}}{4}$
$=100\left(1.732\right)$
$=173.2m$