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Trudy is fishing from a small boat. Her fishing hook is $8\,\text{meters}$ below her, and a fish is swimming at the same depth as the hook, $15\,\text{meters}$ away. How far away is Trudy from the fish? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. Trudy is fishing from a small boat. Her fishing hook is

8\,\text{meters}

below her, and a fish is swimming at the same depth as the hook,

15\,\text{meters}

away. How far away is Trudy from the fish?

\newline

\_\_\_\_\_

meters

Identify Triangle Formed: Identify the triangle formed by Trudy, the hook, and the fish. Trudy's hook is $8$ meters below her, and the fish is $15$ meters horizontally from the hook. This forms a right triangle with the depths as one leg ( $8$ meters), the horizontal distance as the other leg ( $15$ meters), and the distance from Trudy to the fish as the hypotenuse.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the hypotenuse. $\newline$ Using the formula $a^2 + b^2 = c^2$ , where $a = 8$ meters, $b = 15$ meters, and $c$ is the hypotenuse: $\newline$ $8^2 + 15^2 = c^2$ $\newline$ $64 + 225 = c^2$ $\newline$ $289 = c^2$
Solve for Distance: Solve for $c$ , the distance from Trudy to the fish. $\newline$ $c = \sqrt{289}$ $\newline$ $c = 17$ meters.

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