It is found that on walking x meters towards a chimney in a horizontal line through its base, the elevation of its top changes from $30^\circ$ to $60^\circ$. The height of the chimney is

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KollegeApply · Accepted Answer

Let h be the height of chimney AB Given that: angle of elevation changes from angle $\angle$D=$30^\circ$to .$\angle$C=$60^\circ$ Then Distance becomes CD=x and we assume BC=y Here, we have to find the height of chimeny. So we use trigonometric ratios. In a triangle,ABC $\Rightarrow$ tan C=(AB)/(BC) $\Rightarrow$ tan $60^\circ$=(AB)/(BC) $\Rightarrow$ sqrt3=h/y $\Rightarrow$y=h/sqrt3 Again in a triangle ABD, $\Rightarrow$ tan D=(AB)/(BC+CD) $\Rightarrow$ tan $30^\circ$=h/(y+x) $\Rightarrow$1/sqrt3=h/(y+x) $\Rightarrow$sqrt3h=y+x $\Rightarrow$sqrt3h=h/sqrt3+x ["put" y=h/sqrt3] $\Rightarrow$ h(sqrt3-1/sqrt3)=x $\Rightarrow$h=x/(sqrt3-1/sqrt3) $\Rightarrow$h=(sqrt3x)/2 [Solution diagram: 63575_solution_1.png]

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