AYZ is a right triangle (we're given that YA is perpendicular to XZ). So, we can use the pythagorean theorem to find the missing side:
[tex]YA^2+AZ^2=YZ^2[/tex]
But we're also given [tex]YZ = 2AZ[/tex], so we have
[tex]YA^2+AZ^2=(2AZ)^2=4AZ^2[/tex]
Since AZ is half of YZ, which is 10, we deduce AZ=5.
Solving for YA, we have
[tex]YA^2+AZ^2=4AZ^2 \iff YA^2 = 3AZ^2 \iff YA = AZ\sqrt{3} = 5\sqrt{3}[/tex]
