Answer:
[tex]4\sqrt{2}[/tex] units
Step-by-step explanation:
In this right triangle the measure of one interior acute angle is 60°, then the measure of second acute angle is
90°-60°=30°.
The leg that is opposite to the angle of 30° is half of the hypotenuse. If x is opposite to the 30° angle, then the hypotenuse is 2x.
By the Pythagorean theorem,
[tex](4\sqrt{6})^2+x^2=(2x)^2,\\ \\96+x^2=4x^2,\\ \\4x^2-x^2=96,\\ \\3x^2=96,\\ \\x^2=32,\\ \\x=\sqrt{32}=4\sqrt{2}\ units.[/tex]
