Answer:
x = [tex]\sqrt{3}[/tex]
Step-by-step explanation:
the ratio of side to hypotenuse in a right triangle is 1 : [tex]\sqrt{2}[/tex]
in this problem we can use 'x' in place of 1 and [tex]\sqrt{6}[/tex] in place of [tex]\sqrt{2}[/tex] to create a proportion like this:
1/x = [tex]\sqrt{2}[/tex]/[tex]\sqrt{6}[/tex]
cross-multiply to get:
[tex]\sqrt{2}[/tex]·x = [tex]\sqrt{6}[/tex]
x = [tex]\frac{\sqrt{6}}{\sqrt{2}}[/tex]
x = [tex]\sqrt{3}[/tex]
