Answer :
His shadow changing at the instant when he is 24 feet from the pole Is [tex]\frac{95}{13}[/tex]
What do triangles that are similar mean?
The related angle measurements and proportional side lengths of similar triangles are the same.
In this diagram, x represents the distance between the man and the pole, while y represents the distance between the shadow's tip and the pole. My assumption is that the man and the pole are both standing straight up, making the two triangles comparable.
by comparison, [tex]\frac{y-x}{y} = \frac{6}{19}[/tex]
[tex]19(y-x)=6(y)\\19y-19x=6y\\19y-6y=19x\\13y=19x\\y=\frac{19}{13} y[/tex]
differentiate both sides with respect to t or time.
[tex]\frac{dy}{dt}=\frac{19}{13}\frac{dx}{dt}[/tex]
You know [tex]\frac{dx}{dt}[/tex] = 5 ft/s because the man is edging away from the pole at that pace. Find out [tex]\frac{dy}{dt}[/tex] how quickly the shadow's tip is moving.
That Means, [tex]\frac{dy}{dt}= \frac{19}{13} * 5 = \frac{95}{13}[/tex]ft/s
Actually, it doesn't matter how far the man is from the pole because only his speed impacts how quickly his shadow moves.
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