Final answer:
To determine the altitude of the plane after traveling a horizontal distance of 20 miles, the tangent trigonometric function is used along with a conversion from miles to feet. Option B is the correct answer.
Step-by-step explanation:
To calculate the altitude of the Cessna plane after it has traveled a horizontal distance of 20 miles, we need to use the trigonometric function of tangent which relates angles to opposite and adjacent sides in a right triangle. In this case, the angle given is 16 degrees and the adjacent side represents the horizontal distance covered, which is 20 miles. The equation we use is:
- tan(angle) = opposite/adjacent
- tan(16 degrees) = altitude/20 miles
- altitude = 20 miles * tan(16 degrees)
To convert miles to feet, recall that there are 5,280 feet in a mile. So, to find the altitude in feet:
- altitude = 20 miles * 5,280 feet/mile * tan(16 degrees)
- altitude ≈ 20 * 5,280 * 0.2867
- altitude ≈ 30,283.2 feet
After calculating the altitude, we round it to the nearest foot. Given the provided choices, none match our calculated result. Therefore, the question may contain a typo or an error in the provided choices.