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(A) Let the height of the cliff be $h \ m$ and the distance of the observer from the base of the cliff be $x \ m$.From the given information,the heigh

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$30$

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(A) Let the height of the cliff be $h \ m$ and the distance of the observer from the base of the cliff be $x \ m$.From the given information,the height of the tower is $60 \ m$.In the right-angled triangle formed by the cliff and the observer,we have:$	an(30^\circ) = \frac{h}{x} \Rightarrow x = h \cot(30^\circ) = h\sqrt{3}$.In the right-angled triangle formed by the tower and the cliff together,the total height is $(h + 60) \ m$:$	an(60^\circ) = \frac{h + 60}{x} \Rightarrow x = \frac{h + 60}{	an(60^\circ)} = \frac{h + 60}{\sqrt{3}}$.Equating the two expressions for $x$:$h\sqrt{3} = \frac{h + 60}{\sqrt{3}}$$3h = h + 60$$2h = 60$$h = 30 \ m$.

An observer in a boat finds that the angle of elevation of the top of a tower standing on the top of a cliff is $60^\circ$ and that of the top of the cliff is $30^\circ$. If the height of the tower is $60 \ m$,then the height of the cliff is ... $m$.

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