A lighthouse stands $200$ meters tall on a straight coastline. A ship sails directly towards the lighthouse. Let $\theta$ be the angle of elevation of the lighthouse from the ship. Find the rate of change of the angle of elevation $\frac{d\theta }{dx}$ when the ship is $x=300\text{ m}$ away from the lighthouse.

• A. $-0.00344\text{ radians per meter}$
• B. $-0.00154\text{ radians per meter}$
• C. $-0.00308\text{ radians per meter}$
• D. $-0.00054\text{ radians per meter}$

Answer: (B)