REVIOUS ANSWERS ASK YOUR TEACHER An airplane is flying in still air with an airspeed of 475 miles per hour The plane is climbing at an angle of \( 32^{\circ} \). Find the rate (in mi/hr) at which the plane is gaining altitude. (Round your answer to four decimal places.) \begin{tabular}{|} \& \( \mathrm{mi} / \mathrm{hr} \)\end{tabular}

To find the rate at which the airplane is gaining altitude, you can use the sine function. The vertical component (altitude gain) can be calculated using: \[ \text{Altitude Gain Rate} = \text{Airspeed} \times \sin(\theta) \] Where: - Airspeed = 475 mi/hr - \(\theta = 32^{\circ}\) Now calculating: \[ \text{Altitude Gain Rate} = 475 \times \sin(32^{\circ}) \] \[ = 475 \times 0.5299 \quad (\text{approx. value for } \sin(32^\circ)) \] \[ \approx 251.2475 \, \text{mi/hr} \] So, the rate at which the plane is gaining altitude is approximately \( 251.2475 \, \text{mi/hr} \), rounded to four decimal places is: \[ \text{Altitude Gain Rate} \approx 251.2475 \, \text{mi/hr} \]