Step 1 :Given that the airplane is traveling at a speed of 600 mph, the initial altitude is 7.2 miles, the angle of descent is 1 degree, and the time of descent is 10 minutes.
Step 2 :First, convert the time of descent from minutes to hours. Since there are 60 minutes in an hour, \(10 \text{ min} = \frac{10}{60} = 0.16666666666666666 \text{ hours}\).
Step 3 :Next, calculate the distance traveled by the airplane. The distance is the speed of the airplane times the time of travel, so \(\text{distance} = 600 \text{ mph} \times 0.16666666666666666 \text{ hours} = 100 \text{ miles}\).
Step 4 :Then, calculate the change in altitude. The change in altitude is the sine of the angle of descent times the distance traveled. Since the sine of 1 degree is approximately 0.01745240643728351, \(\text{change in altitude} = 0.01745240643728351 \times 100 \text{ miles} = 1.7452406437283512 \text{ miles}\).
Step 5 :Finally, calculate the new altitude. The new altitude is the initial altitude minus the change in altitude, so \(\text{new altitude} = 7.2 \text{ miles} - 1.7452406437283512 \text{ miles} = 5.5 \text{ miles}\).
Step 6 :\(\boxed{5.5}\) miles is the new altitude of the airplane after it has descended for 10 minutes at a speed of 600 mph and an angle of descent of 1 degree.