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A flying squirrel lives in a nest that is $12$ feet high in a tree. To reach a fallen acorn that is $16$ feet from the base of the tree, how far will the flying squirrel have to glide? $\newline$ $\_\_\_\_$ feet

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Pythagorean theorem: word problems

Full solution

Q. A flying squirrel lives in a nest that is

12

feet high in a tree. To reach a fallen acorn that is

16

feet from the base of the tree, how far will the flying squirrel have to glide?

\newline

\_\_\_\_

feet

Identify Problem: Identify the problem: We need to find the distance the squirrel must glide from its nest to the acorn. This forms a right triangle with the tree height as one leg ( $12$ feet) and the distance from the tree to the acorn as the other leg ( $16$ feet).
Apply Theorem: Apply the Pythagorean Theorem: Let $d$ be the distance the squirrel glides. According to the theorem, the sum of the squares of the legs equals the square of the hypotenuse. So, $12^2 + 16^2 = d^2$ .
Calculate Squares: Calculate the squares: $12^2 = 144$ and $16^2 = 256$ . Add these to find $d^2$ . $144 + 256 = 400$ .
Solve for Distance: Solve for $d$ : Take the square root of both sides to find $d$ . $\sqrt{400} = d$ . Therefore, $d = 20$ .

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