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A small Cessna plane takes off from an airport and rises uniformly at an angle of 16 degrees with the horizontal ground. After it has traveled over a horizontal distance of 20 miles, what is the altitude of the plane to the nearest foot?

a) 5,669 feet
b) 5,096 feet
c) 6,320 feet
d) 4,502 feet

User Dwich
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1 Answer

3 votes

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.

User Ryan Brownell
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