An airplane traveling at $600 \mathrm{mph}$ at a cruising altitude of $7.2 \mathrm{mi}$ begins its descent. If the angle of descent is $1^{\circ}$ from the horizontal, determine the new altitude after $10 \mathrm{~min}$. Round to the nearest tenth of a mile.
The new altitude is approximately $\mathrm{mi}$.

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.