To solve for the length of the unknown leg in a right triangle using the Pythagorean theorem, follow these steps:
1. Identify the given values:
- One leg, [tex]\( b \)[/tex], is 8 feet long.
- The hypotenuse, [tex]\( c \)[/tex], is 10 feet long.
- We need to find the length of the other leg, [tex]\( a \)[/tex].
2. Recall the Pythagorean theorem:
- The Pythagorean 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 legs ([tex]\( a \)[/tex] and [tex]\( b \)[/tex]):
[tex]\[
a^2 + b^2 = c^2
\][/tex]
3. Rearrange the Pythagorean theorem to solve for the unknown leg [tex]\( a \)[/tex]:
- [tex]\( a^2 = c^2 - b^2 \)[/tex]
4. Substitute the known values into the equation:
- [tex]\( c = 10 \)[/tex] feet
- [tex]\( b = 8 \)[/tex] feet
[tex]\[
a^2 = 10^2 - 8^2
\][/tex]
5. Calculate the squares of the known values:
- [tex]\( 10^2 = 100 \)[/tex]
- [tex]\( 8^2 = 64 \)[/tex]
[tex]\[
a^2 = 100 - 64
\][/tex]
6. Subtract the values:
[tex]\[
a^2 = 36
\][/tex]
7. Take the square root of both sides to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \sqrt{36} = 6
\][/tex]
Thus, the length of the unknown leg is 6 feet.
The best answer is:
B. [tex]$6 ft$[/tex].
