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Use the Pythagorean theorem to solve the question

Use the Pythagorean theorem to solve the question-example-1

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Answer:

The Pythagorean theorem shows us that Plane B is closer to the base of the airport tower as it is approximately 8000 ft away from the base of the airport tower, while Plane A is approximately 20000 ft away from the base of the airport tower.

Explanation:

The distance between the two planes and the base of the airport tower creates a right triangle.

In the first triangle,

  • The ground is one side,
  • the height of Plane A is another side,
  • and the distance between Plane A and the base of the airport tower is a third side (specifically, the hypotenuse).

The Pythagorean theorem is given by:

a^2 + b^2 = c^2, where

  • a and b are the shorter sides of a triangle called legs,
  • and c is the longest side called the hypotenuse (always opposite the right angle).

Finding the distance between Plane A and the base of the airport tower:

For the triagle with Plane A, we can plug in 5 and 20000 for a and b in the Pythagorean theorem, allowing us to solve for c (the hypotenuse or contextually, the distance between Plane A and the base of the airport tower):

5^2 + 20000^2 = c^2

25 + 400000000 = c^2

400000025 = c^2

20000.00063 = c

20000 ≈ c

Thus, the distance between Plane A and the base of the airport to

Finding the distance between Plane B and the base of the airport tower:

Note that in triangle B, one side is 7 km as 5 + 2 = 7

Thus, for the triangle with Plane B, we can plug in 7 and 8000 for a and b in the Pythagorean theorem, to solve for c (the hypotenuse, or contextually, the distance between Plane B and the base of the airport tower):

7^2 + 8000^2 = c^2

49 + 64000000 = c^2

64000049 = c^2

8000.003062 = c

8000 ≈ c

Thus, Plane B is closer to the base of the airport tower as it is approximately 8000 ft away from the base of the airport tower, while Plane A is approximately 20000 ft away from the base of the airport tower.

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