Question

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

Answer 1

Let one boat is at $B$

Other boat is at $C$

Also $BC=x$ meters

Now $\cot \alpha =\frac{OB}{AO}$

$\therefore OB=h\cot \alpha$

similarly $OC=h\cot \beta$

$\therefore h\cot \alpha +h\cot \beta =BC=x$

$\therefore h=\frac{xmeters}{\cot \alpha +\cot \beta }\to$ hence proved

Now,

$\alpha ={60}^{\circ }$

$\beta ={45}^{\circ }$

$x=250m$

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

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

$\therefore$ Height $\left(h\right)$ is $\frac{250\sqrt{3}}{\sqrt{3}+1}$ meters