Question

which equation can be solved to find one of the missing side lengths in the triangle? cos(60°) = 12/a cos(60°) = 12/b cos(60°) = b/a

Explanation:

Step1: Recall cosine - ratio definition

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 side adjacent to $\angle B$ is $a$ and the hypotenuse is $12$.

Step2: Apply cosine formula

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

Answer:

None of the given options are correct. The correct equation to find side $a$ is $\cos(60^{\circ})=\frac{a}{12}$. If we rewrite the options to be correct, the correct form based on the cosine ratio for $\angle B$ in the right - triangle should be $\cos(60^{\circ})=\frac{a}{12}$ (not in the given choices). If we consider the reciprocal relationship, we can also say $\sec(60^{\circ})=\frac{12}{a}$. But among the given options, there is an error as written.