A streetlight of height $H$ is fixed at point $A$ on the ground. A person walks away from the streetlight along a straight path at a constant speed. Let $B$ be the point where the person is currently standing, and let $C$ be the distance between points $A$ and $B$ on the ground. Define $\theta$ as the angle between the streetlight and the line connecting the top of the streetlight to point $B$. Find $\frac{d\theta }{dC}$.

• A. $\frac{d\theta }{dC}=-\frac{C}{H^2+C^2}$
• B. $\frac{d\theta }{dC}=-\frac{H}{H^2+C^2}$
• C. $\frac{d\theta }{dC}=\frac{C}{H^2+C^2}$
• D. $\frac{d\theta }{dC}=\frac{H}{H^2+C^2}$

Answer: (D)