To find the length of each leg in a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle given the hypotenuse, we can use the properties of this type of triangle. In a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle, both legs are of equal length, and the relationship between the lengths of the legs and the hypotenuse is such that each leg is [tex]\(\frac{1}{\sqrt{2}}\)[/tex] times the length of the hypotenuse.
Given:
Hypotenuse = [tex]\(7\sqrt{2}\)[/tex]
We want to find the length of each leg. To do that, we divide the hypotenuse by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
\text{Length of each leg} = \frac{\text{Hypotenuse}}{\sqrt{2}}
\][/tex]
[tex]\[
\text{Length of each leg} = \frac{7\sqrt{2}}{\sqrt{2}}
\][/tex]
Simplifying the fraction:
[tex]\[
\text{Length of each leg} = 7
\][/tex]
Therefore, the length of each leg in the triangle is 7.
The correct answer is: 7
