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What is the length of the missing leg? If necessary, round to the nearest tenth.

a=

◻ yards

What is the length of the missing leg? If necessary, round to the nearest tenth. $\newline$ $a=$ $\newline$ $\square$ yards

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Pythagorean theorem

Full solution

Q. What is the length of the missing leg? If necessary, round to the nearest tenth.

\newline

a=

\newline

\square

yards

Identify Given Lengths: Identify the given lengths of the triangle's sides. We know the hypotenuse is $29$ yards and one leg is $21$ yards.
Use Pythagorean Theorem: Use the Pythagorean Theorem to find the missing leg, $a$ . The theorem states that $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse and $a$ and $b$ are the legs.
Plug in Values: Plug in the known values into the Pythagorean Theorem. So we have $a^2 + 21^2 = 29^2$ .
Calculate Squares: Calculate the squares of the known sides. $21^2 = 441$ and $29^2 = 841$ .
Subtract to Find $a^2$ : Subtract the square of the known leg from the square of the hypotenuse to find $a^2$ . So, $a^2 = 841 - 441$ .
Perform Subtraction: Perform the subtraction to find $a^2$ . $a^2 = 841 - 441 = 400$ .
Take Square Root: Take the square root of $a^2$ to find the value of $a$ . $\sqrt{a^2} = \sqrt{400}$ .
Calculate Final Value: Calculate the square root of $400$ to find $a$ . $a = 20$ .

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