To determine the length of the missing leg (a) in a right triangle where the two other lengths are given (13 mm and 12 mm), we can use the Pythagorean theorem. This theorem states that in a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.
Assuming 13 mm is the hypotenuse and 12 mm is one leg, we can find the missing leg \( a \) using the formula:
\[ c^2 = a^2 + b^2 \]
Where:
- \( c \) is the hypotenuse (13 mm),
- \( a \) is one leg (12 mm),
- \( b \) is the missing leg.
Rearranging the formula to solve for \( b \):
\[ b^2 = c^2 - a^2 \]
Substituting the known values:
\[ b^2 = 13^2 - 12^2 \]
Calculating the squares:
\[ b^2 = 169 - 144 \] \[ b^2 = 25 \]
Taking the square root to find \( b \):
\[ b = \sqrt{25} = 5 \text{ mm} \]
Therefore, the length of the missing leg \( b \) is 5 mm.