Answer: [tex]6\sqrt{2}\ in[/tex]
Step-by-step explanation:
Given: In a 45-45-90 triangle, the length of one of the legs= 6 in.
Let h be the hypotenuse of the given right triangle.
Since the two angles are equal (45°) in the given right triangle,Moreover in a triangle the side opposite to the equal angles are equal.
Therefore, the other leg of given right triangle = 6 in.
Thus by Pythagoras theorem, we get
[tex]h^2=6^2+6^2=36+36\\\\\Rightarrow\ h^2=72\\\\\Rightarrow h=\sqrt{72}\\\\\Rightarrow h=6\sqrt{2}\ in[/tex]
Hence, the length of its hypotenuse = [tex]6\sqrt{2}\ in[/tex]
