To find the length of the other leg in a right triangle where the hypotenuse is 17 and one leg is 8, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle. In this case:
- \( c = 17 \)
- \( a = 8 \)
- \( b \) is the unknown leg.
Plugging in the values we have:
\[ 8^2 + b^2 = 17^2 \]
Calculating the squares:
\[ 64 + b^2 = 289 \]
Now, solve for \( b^2 \) by subtracting 64 from both sides:
\[ b^2 = 289 - 64 \] \[ b^2 = 225 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{225} \] \[ b = 15 \]
Thus, the length of the other leg is 15.