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(B) Let the ladder be represented by the hypotenuse of a right-angled triangle formed by the ladder,the wall,and the floor.Let $x$ be the distance of

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$\frac{3}{2} 	ext{ ft/sec}$

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(B) Let the ladder be represented by the hypotenuse of a right-angled triangle formed by the ladder,the wall,and the floor.Let $x$ be the distance of the man from the wall along the ladder.Let $y$ be the horizontal distance of the man from the wall.The angle between the ladder and the wall is $	heta = 30^\circ$.From trigonometry,the horizontal distance $y$ is given by $y = x \sin(	heta)$.Here,$	heta = 30^\circ$,so $y = x \sin(30^\circ) = x 	imes \frac{1}{2}$.Differentiating with respect to time $t$,we get $\frac{dy}{dt} = \frac{dx}{dt} 	imes \frac{1}{2}$.Given that the rate of climbing the ladder is $\frac{dx}{dt} = 3 	ext{ ft/sec}$.Therefore,the rate at which he approaches the wall is $\frac{dy}{dt} = 3 	imes \frac{1}{2} = \frac{3}{2} 	ext{ ft/sec}$.

$A$ ladder makes an angle of $30^\circ$ with the wall. $A$ man is climbing the ladder at the rate of $3 \text{ ft/sec}$. What is the rate at which he is approaching the wall?

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