Question

Find $h$ if $\alpha ={60}^o,\beta ={45}^o$ and $x=250m$.

• A. $129.3m$
• B. $136.4m$
• C. $158.5m$
• D. $171.2m$

Answer 1

Answer: (C)

$158.5m$

$\alpha ={60}^o$
Hence
$\cot \alpha =\frac{1}{\sqrt{3}}$
$\beta ={45}^o$
$\cot \beta =1$
Hence
$h=\frac{x}{\cot \alpha +\cot \beta }$

$=\frac{250}{1+\frac{1}{\sqrt{3}}}$

$=\frac{250\sqrt{3}}{1+\sqrt{3}}$

$=\frac{250\sqrt{3}(\sqrt{3}-1)}{2}$

$=125\left(1.732\right)\left(0.732\right)$
$=158.5m$