To find the length of the other side (let’s call it \( a \)) in a right triangle with a hypotenuse \( c \) and a base \( b \), we can use the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
In this case, the hypotenuse \( c = 10 \) inches and the base \( b = 8 \) inches. Plugging those values into the formula gives:
\[ 10^2 = a^2 + 8^2 \]
Calculating the squares:
\[ 100 = a^2 + 64 \]
Now, isolate \( a^2 \):
\[ a^2 = 100 - 64 \] \[ a^2 = 36 \]
Taking the square root of both sides to find \( a \):
\[ a = \sqrt{36} = 6 \]
Thus, the length of the other side is \( 6 \) inches.
This means the correct option is:
b = 6 in.