A car departs from a town and travels southeast at a constant speed of 40 mi/hr 40~\text{mi}\text{/}\text{hr} 40 mi / hr . At 1:00 \text{1:00} PM, the car passes its closest point to a tracking station, which is located 3 mi 3~\text{mi} east of the town. What is the rate of change of the angle θ \theta between the tracking station and the car at 2:00 \text{2:00} PM if the car continues on its path at the same speed? Use the Law of Sines and assume that the path of the car is straight. Round the answer to three decimal places.

d θ d t ≈ 0.053 r a d h r \frac{d\theta}{dt}\approx0.053~\frac{\mathrm{rad}}{\mathrm{hr}}

d θ d t ≈ 0.027 rad hr \frac{d\theta}{dt}\approx0.027~\frac{\text{rad}}{\text{hr}}

d θ d t ≈ 0.071 r a d h r \frac{d\theta}{dt}\approx0.071~\frac{\mathrm{rad}}{\mathrm{hr}}

d θ d t ≈ 0.095 r a d h r \frac{d\theta}{dt}\approx0.095~\frac{\mathrm{rad}}{\mathrm{hr}}

A car departs from a town and travels southeast at...

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