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Find the length of the third side. If necessary, round to the nearest tenth.

Find the length of the third side. If necessary, round to the nearest tenth.

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Pythagorean theorem

Full solution

Q. Find the length of the third side. If necessary, round to the nearest tenth.

Identify Known Distances: Identify the known distances and the triangle sides they represent. $\newline$ Adam to Whitney = $21$ feet (leg $b$ ), Whitney to Bella = $29$ feet (hypotenuse $c$ ), Adam to Bella = ? (leg $a$ ).
Apply Pythagorean Theorem: Apply the Pythagorean Theorem: $a^2 + b^2 = c^2$ . $\newline$ Here, $a^2 + 21^2 = 29^2$ .
Substitute and Simplify: Substitute the known values and simplify. $a^2 + 441 = 841$ .
Solve for $a^2$ : Solve for $a^2$ . $\newline$ $a^2 = 841 - 441$ , $\newline$ $a^2 = 400$ .
Find Value of a: Find the value of $a$ by taking the square root of $400$ . $a = \sqrt{400}$ , $a = 20$ .

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