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A flying squirrel's nest is $8\,\text{meters}$ high in a tree. From its nest, the flying squirrel glides $10\,\text{meters}$ to reach an acorn that is on the ground. How far is the acorn from the base of the tree? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. A flying squirrel's nest is

8\,\text{meters}

high in a tree. From its nest, the flying squirrel glides

10\,\text{meters}

to reach an acorn that is on the ground. How far is the acorn from the base of the tree?

\newline

\_\_\_\_\_

meters

Identify Height and Distance: Identify the height of the nest and the distance the squirrel glides. Height of the nest: $8$ meters, Distance glided: $10$ meters.
Form Right Triangle: Recognize the right triangle formed by the height of the nest, the distance to the acorn, and the glide distance. The height of the nest is one leg, the distance from the base of the tree to the acorn is the other leg, and the glide distance is the hypotenuse.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem: $(\text{Leg1})^2 + (\text{Leg2})^2 = (\text{Hypotenuse})^2$ . Here, $\text{Leg1}$ is $8$ meters, $\text{Hypotenuse}$ is $10$ meters.
Plug in Values: Plug in the values: $8^2 + x^2 = 10^2$ . Simplify the squares: $64 + x^2 = 100$ .
Solve for $x^2$ : Solve for $x^2$ : $x^2 = 100 - 64$ . $x^2 = 36$ .
Find $x$ : Find $x$ by taking the square root of $36$ . $x = \sqrt{36}$ . $x = 6$ meters.

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