Answer:
10 units
Step-by-step explanation:
Given triangle is right triangle with acute angle of measure 45°. Then second acute angle has measure
90°-45°=45°.
This means that given right triangle is isosceles triangle. Therefore the second leg is also [tex]5\sqrt{2}[/tex] units. By the Pythagorean theorem,
[tex]c^2=(5\sqrt{2})^2+(5\sqrt{2})^2,\\ \\c^2=50+50,\\ \\c^2=100,\\ \\c=10\ \text{units}.[/tex]
