A current $I_0$ flows along a straight wire segment that is $5$ m long and aligned with the $x-$axis. A field point, $P$ lies in the $xy-$plane, such that the angle it presents from the left end of the wire is $53\mathrm{.}13$ and from the right end: $36\mathrm{.}87.$ The positive $z-$axis emerges from the page.

We will determine the magnetic field at the field point produced by the current in the wire.

$($a$)$ Determine the perpendicular distance from the wire to the field point.

$($b$)$ Compute the magnetic field produced at the field point by the current in the wire.