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Rachel is sitting in a tree $15$ feet above the ground. A minute ago, she spotted a skunk $40$ feet from the base of the tree walking closer to her. Now, the skunk is $20$ feet from the base of the tree. The diagonal line from Rachel to the skunk is the distance between them. How much closer is the skunk to Rachel now than it was a minute ago? $\newline$ If necessary, round your answer to the nearest tenth. $\newline$ $\_\_\_\_$ feet $\newline$

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Pythagorean theorem

Full solution

Q. Rachel is sitting in a tree

15

feet above the ground. A minute ago, she spotted a skunk

40

feet from the base of the tree walking closer to her. Now, the skunk is

20

feet from the base of the tree. The diagonal line from Rachel to the skunk is the distance between them. How much closer is the skunk to Rachel now than it was a minute ago?

\newline

If necessary, round your answer to the nearest tenth.

\newline

\_\_\_\_

feet

\newline

Identify Distances: Identify the distances involved in the problem. Rachel is $15$ feet above the ground, and the skunk's initial distance from the tree is $40$ feet, now reduced to $20$ feet.
Calculate Initial Distance: Calculate the initial diagonal distance from Rachel to the skunk using the Pythagorean theorem. Initial distance = $\sqrt{15^2 + 40^2} = \sqrt{225 + 1600} = \sqrt{1825}$ .
Calculate New Distance: Calculate the new diagonal distance from Rachel to the skunk using the Pythagorean theorem. New distance = $\sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625}$ .
Find Difference: Subtract the new distance from the initial distance to find out how much closer the skunk is now. Difference = $\sqrt{1825} - \sqrt{625} = 42.7 - 25 = 17.7$ feet.

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