Monochromatic light at $559$ nm illuminates a diffraction grating with $315$ lines$/$mm$.$ Determine the angle to the first$-$order maximum, the highest order that can be observed with this grating at the given wavelength, and the angle to this highest$-$order maximum.

HINT

$($a$)$

the angle to the first$-$order maximum $($in degrees$)$

$$

$($b$)$

the highest order that can be observed with this grating at the given wavelength

$($c$)$

the angle to this highest$-$order maximum $($in degrees$)$