To find the length of one leg of a right triangle given the length of the other leg and the hypotenuse, we use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse ([tex]\(c\)[/tex]) is equal to the sum of the squares of the lengths of the other two sides ([tex]\(a\)[/tex] and [tex]\(b\)[/tex]):
[tex]\[ c^2 = a^2 + b^2 \][/tex]
In this problem:
- The length of one leg ([tex]\(a\)[/tex]) is 8 feet.
- The hypotenuse ([tex]\(c\)[/tex]) is 10 feet.
- We need to find the length of the other leg ([tex]\(b\)[/tex]).
First, rearrange the Pythagorean theorem to solve for [tex]\(b\)[/tex]:
[tex]\[ b^2 = c^2 - a^2 \][/tex]
Now, substitute the given values into the equation:
[tex]\[ b^2 = 10^2 - 8^2 \][/tex]
[tex]\[ b^2 = 100 - 64 \][/tex]
[tex]\[ b^2 = 36 \][/tex]
Next, take the square root of both sides to solve for [tex]\(b\)[/tex]:
[tex]\[ b = \sqrt{36} \][/tex]
[tex]\[ b = 6 \][/tex]
Thus, the length of the leg is [tex]\(6\)[/tex] feet.
Therefore, the best answer is:
A. [tex]$6 ft$[/tex].
