Finding the Length of the Adjacent Side in Right Triangle

Consider a right triangle where one of the angles is given as $ heta$. The lengths of the opposite side to $ heta$ is represented as $a$, and the length of the adjacent side is represented as $b$. The sine and cosine of the angle $ heta$ can be defined as:

$ ext{sine}( heta) = \frac{a}{c}$ and $ ext{cosine}( heta) = \frac{b}{c}$, where $c$ is the length of the hypotenuse.

Let $ heta = 30^{ ext{o}}$. If we know that the lengths of the opposite side $a$ is equal to $5$, what is the length of the adjacent side $b$? Assume the hypotenuse $c$ remains constant.

Which of the following represents the length of the adjacent side $b$?