Answer: [tex]5\sqrt{2}\ in[/tex]
Step-by-step explanation:
Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.
Let H be the hypotenuse of the given right triangle.
Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.
Therefore, the other leg of given right triangle = 5 in.
Now applying Pythagoras theorem, we get
[tex]H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=\sqrt{50}\\\\\Rightarrow H=5\sqrt{2}\ in[/tex]
Hence, the length of the hypotenuse = [tex]5\sqrt{2}\ in[/tex]
