which equation can be solved to find one of the missing side lengths in the triangle?\ncos(60°) =…

Explanation:

Step1: Recall cosine definition in right - triangle

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $ABC$ with right - angle at $C$, for $\angle B = 60^{\circ}$, the adjacent side to $\angle B$ is side $a$ and the hypotenuse is side $AB = 12$ units.

Step2: Apply cosine formula

We know that $\cos(60^{\circ})=\frac{a}{12}$, which can be rewritten as $\cos(60^{\circ})=\frac{a}{12}\Rightarrow a = 12\cos(60^{\circ})$.

Answer:

$\cos(60^{\circ})=\frac{a}{12}$ (equivalent to the first option $\cos(60^{\circ})=\frac{12}{a}$ is incorrect, the correct form should be $\cos(60^{\circ})=\frac{a}{12}$; the second option $\cos(60^{\circ})=\frac{12}{b}$ is incorrect as $b$ is not related to the cosine of $\angle B$ in this way; the third option $\cos(60^{\circ})=\frac{b}{a}$ is incorrect according to the cosine definition for $\angle B$). So the correct equation from the given options (after correction) is $\cos(60^{\circ})=\frac{a}{12}$.