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#

Where #a# and #b# are legs of a right triangle and #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 + 49 = 100#

#a^2 + 49 - color(red)(49) = 100 - color(red)(49)#

#a^2 = 51#

#sqrt(a^2) = sqrt(51)#

#a = sqrt(51) = 7.14# rounded to the nearest hundredth.