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Lúcia was given this problem:$\newline$A $15$-meter ladder is leaning against a wall. The distance $y(t)$ between the top of the ladder and the ground is decreasing at a rate of $6$ meters per minute. At a certain instant $t_{0}$, the bottom of the ladder is a distance $x\left(t_{0}\right)$ of $12$ meters from the wall. What is the rate of change of the angle $\theta(t)$ between the ground and the ladder at that instant?$\newline$Which equation should Lúcia use to solve the problem?$\newline$Choose $1$ answer:$\newline$(A) $\sin [\theta(t)]=\frac{y(t)}{15}$$\newline$(B) $\theta(t)=\frac{x(t) \cdot y(t)}{2}$$\newline$(C) $\theta(t)+x(t)+y(t)=180$$\newline$(D) $[\theta(t)]^{2}=[x(t)]^{2}+[y(t)]^{2}$