To find the length of the other leg of the right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this is stated as:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where [tex]\( c \)[/tex] is the hypotenuse, and [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the legs of the triangle. In our case, we are given one leg [tex]\( a = 7 \)[/tex] units and the hypotenuse [tex]\( c = 25 \)[/tex] units. We need to find the length of the other leg, which we will call [tex]\( b \)[/tex].
Step-by-step solution:
1. Write down the Pythagorean theorem with the given values:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
[tex]\[ 7^2 + b^2 = 25^2 \][/tex]
2. Square the given values:
[tex]\[ 49 + b^2 = 625 \][/tex]
3. Subtract 49 from both sides to solve for [tex]\( b^2 \)[/tex]:
[tex]\[ b^2 = 625 - 49 \][/tex]
[tex]\[ b^2 = 576 \][/tex]
4. Take the square root of both sides to solve for [tex]\( b \)[/tex]:
[tex]\[ b = \sqrt{576} \][/tex]
[tex]\[ b = 24 \][/tex]
So, the length of the other leg is [tex]\( 24 \)[/tex] units.
Therefore, the correct answer is:
24 units
