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(A) Let the height of the tower be $h$ and the initial shadow length be $x$. When the angle of elevation is $30^{\circ},$ $	an(30^{\circ}) = h/x \imp

Vedclass · Accepted Answer

$43.30$

Vedclass · Answer

(A) Let the height of the tower be $h$ and the initial shadow length be $x$. When the angle of elevation is $30^{\circ},$ $	an(30^{\circ}) = h/x \implies 1/\sqrt{3} = h/x \implies x = h\sqrt{3}$. When the angle of elevation is $60^{\circ},$ the shadow length becomes $x - 50$. So,$	an(60^{\circ}) = h/(x - 50) \implies \sqrt{3} = h/(x - 50) \implies x - 50 = h/\sqrt{3}$. Substituting $x = h\sqrt{3}$ into the equation: $h\sqrt{3} - 50 = h/\sqrt{3}$. Multiplying by $\sqrt{3}$: $3h - 50\sqrt{3} = h \implies 2h = 50\sqrt{3} \implies h = 25\sqrt{3}$. Using $\sqrt{3} \approx 1.732,$ $h = 25 	imes 1.732 = 43.30\, m$.

When the angle of elevation of the sun increases from $30^{\circ}$ to $60^{\circ},$ the shadow of a tower decreases by $50\, m .$ Find the height of the tower in $m$.

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