Answer is: option3

Solution:

Given

\[ \frac{dy}{dt} = 80 \text{ feet/min} \]

\[ \theta = \frac{\pi}{6} \]

\[ \tan \frac{\pi}{6} = \frac{y}{300} \]

\[ y = 300 \tan \frac{\pi}{6} = 300 \times \frac{1}{\sqrt{3}} = 100 \sqrt{3} \]

\[ \tan \theta = \frac{y}{300} \]

\[ y = 300 \tan \theta \]

Taking derivative on both sides:

\[ \frac{dy}{dt} = 300 \sec^2 \theta \frac{d\theta}{dt} \]

\[ 80 = 300 \times \sec^2 \left(\frac{\pi}{6}\right) \times \frac{d\theta}{dt} \]

\[ 80 = 300 \times \frac{4}{3} \times \frac{d\theta}{dt} \]

\[ \frac{d\theta}{dt} = \frac{80 \times 3}{300 \times 4} = \frac{1}{5} = 0.2 \]