To find the other side length of a right triangle when you know the hypotenuse and one side length, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the hypotenuse,
- \( a \) and \( b \) are the other two sides.
In this case, we have:
- \( c = 10 \)
- \( a = 6 \) (the side length you know)
Now, substitute the known values into the equation:
\[ 6^2 + b^2 = 10^2 \] \[ 36 + b^2 = 100 \]
Now, isolate \( b^2 \):
\[ b^2 = 100 - 36 \] \[ b^2 = 64 \]
Now, take the square root of both sides:
\[ b = \sqrt{64} \] \[ b = 8 \]
So, the other side length is 8.