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(D) Let the height of the tower be $h$ and the length of the shadow when the Sun's altitude is $45^{\circ}$ be $x$.In $	riangle BAD$,$	an 45^{\circ}

Vedclass · Accepted Answer

$30(\sqrt{3}+1) \ m$

Vedclass · Answer

(D) Let the height of the tower be $h$ and the length of the shadow when the Sun's altitude is $45^{\circ}$ be $x$.In $	riangle BAD$,$	an 45^{\circ} = \frac{h}{x}$ $\Rightarrow 1 = \frac{h}{x}$ $\Rightarrow x = h$.When the Sun's altitude is $30^{\circ}$,the shadow length is $x + 60$.In $	riangle BAC$,$	an 30^{\circ} = \frac{h}{x+60} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{h+60}$.$\Rightarrow h + 60 = h\sqrt{3}$$\Rightarrow h(\sqrt{3} - 1) = 60$$\Rightarrow h = \frac{60}{\sqrt{3}-1} 	imes \frac{\sqrt{3}+1}{\sqrt{3}+1}$$\Rightarrow h = \frac{60(\sqrt{3}+1)}{3-1} = \frac{60(\sqrt{3}+1)}{2} = 30(\sqrt{3}+1) \ m$.

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

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