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.