In a right triangle, if one leg measures $4$ ft and the hypotenuse measures $8$ ft, what is the length of the other leg $r$?

• A. $4$ ft
• B. $\sqrt{48}$ ft
• C. $8$ ft
• D. $16$ ft

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle: one leg is 4 ft, the hypotenuse is 8 ft, and the other leg is unknown, denoted as \( r \).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: \( c^2 = a^2 + b^2 \). Here, \( c = 8 \), one leg \( a = 4 \), and the other leg \( b = r \).
3. Set up the equation using the Pythagorean theorem: \( 8^2 = 4^2 + r^2 \).
4. Calculate the squares of the known sides: \( 64 = 16 + r^2 \).
5. Isolate \( r^2 \) by subtracting 16 from both sides: \( r^2 = 64 - 16 \), then express \( r \) as \( r = \sqrt{64 - 16} \).