To determine the length of the other leg in a right triangle when one leg and the hypotenuse are given, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse ([tex]\( c \)[/tex]) is equal to the sum of the squares of the other two legs ([tex]\( a \)[/tex] and [tex]\( b \)[/tex]). Mathematically, this is expressed as:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Given:
- One leg ([tex]\( a \)[/tex]) = 7 units
- Hypotenuse ([tex]\( c \)[/tex]) = 25 units
We need to find the length of the other leg ([tex]\( b \)[/tex]).
First, we rearrange the Pythagorean theorem to solve for [tex]\( b \)[/tex]:
[tex]\[ b^2 = c^2 - a^2 \][/tex]
Substituting the given values:
[tex]\[ b^2 = 25^2 - 7^2 \][/tex]
Next, we calculate each term:
[tex]\[ 25^2 = 625 \][/tex]
[tex]\[ 7^2 = 49 \][/tex]
Subtracting these results:
[tex]\[ b^2 = 625 - 49 \][/tex]
[tex]\[ b^2 = 576 \][/tex]
To find [tex]\( b \)[/tex], we take the square root of [tex]\( b^2 \)[/tex]:
[tex]\[ b = \sqrt{576} \][/tex]
[tex]\[ b = 24 \][/tex]
Hence, the length of the other leg is:
[tex]\[ \boxed{24 \text{ units}} \][/tex]
