To find the length of the unknown leg \( a \) in the right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse and \( b \) is the length of the known leg.
Here:
- \( c = \sqrt{73} \)
- \( b = 8 \)
- \( a \) is the unknown leg.
First, we can express the Pythagorean theorem in terms of our values:
\[ a^2 + 8^2 = (\sqrt{73})^2 \]
Calculating \( 8^2 \) and \( (\sqrt{73})^2 \):
\[ a^2 + 64 = 73 \]
Now, we can solve for \( a^2 \):
\[ a^2 = 73 - 64 \]
\[ a^2 = 9 \]
Now, taking the square root of both sides:
\[ a = \sqrt{9} = 3 \]
Therefore, the length of the unknown leg \( a \) is 3 feet.
The correct answer is 3 ft.