Finding Length in Right Triangle with Trigonometry

In triangle $ABC$, angle $A$ is a right angle, and the lengths of sides $AB$ and $AC$ are $x$ and $4$ respectively. If the sine of angle $B$ is given by the formula

$ ext{sine}(B) =\frac{AC}{AB}$,

give an expression for the value of $x$ in terms of trigonometric values. Additionally, if $BC$ has a length equal to $10$ units, find the value of $x$. Round your answer to two decimal places.