see the attached figure with letters to better understand the problem
Step 1
Find the length of BD
we know that
In the right triangle ABD
BD=AD ------> because is a [tex]45\°-90\°-45\°[/tex] triangle
so
[tex]BD=5\ units[/tex]
Step 2
Find the length of BC
In the right triangle BCD
[tex]sin(30\°)=\frac{BD}{BC}[/tex]
we have
[tex]sin(30\°)=\frac{1}{2}[/tex]
[tex]BD=5\ units[/tex]
[tex]BC=x\ units[/tex]
substitute the values and solve for x
[tex]\frac{1}{2}=\frac{5}{x}\\ \\x=5*2 \\ \\x=10\ units[/tex]
therefore
the answer is
The length of x is [tex]10\ units[/tex]
