Answer
$x\approx 5.4$
Work Step by Step
When a diameter of a circle is perpendicular to a chord, then it will bisect the chord and its arc.
Apply Pythagorean Theorem.
$(3.6)^2+(4)^2=x^2 \\ x^2=28.96\\ x =\sqrt {28.96}$
Therefore, $x\approx 5.4$