Using the Pythagorean Theorem, how do you find the length of a leg of a right triangle if the other leg is 7 feet long and the hypotenuse is 10 feet long?

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Answer 1 · 2017-01-26T22:36:36

See the entire solution process below:

The Pythagorean Theorem states:

$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

Where $a$ $a$ and $b$ $b$ are legs of a right triangle and $c$ $c$ is the hypotenuse.

Substituting the values for the problem for one of the legs and the hypotenuse and the solving for the other leg gives:

$a^{2} + 7^{2} = 10^{2}$ $a^2 + 7^2 = 10^2$

$a^{2} + 49 = 100$ $a^2 + 49 = 100$

$a^{2} + 49 - 49 = 100 - 49$ $a^2 + 49 - color(red)(49) = 100 - color(red)(49)$

$a^{2} = 51$ $a^2 = 51$

$\sqrt{a^{2}} = \sqrt{51}$ $sqrt(a^2) = sqrt(51)$

$a = \sqrt{51} = 7.14$ $a = sqrt(51) = 7.14$ rounded to the nearest hundredth.