Final answer:
To calculate how far the airplane is from its takeoff point after its 3D journey, we use the Pythagorean theorem twice: first for the 2D ground distance and then including altitude. The final calculated distance is approximately 16.4 km, which does not match the given answer choices.
Step-by-step explanation:
The question asks how far an airplane is from its takeoff point after traveling 12km due west, 10km due north, and 5 km above ground. To solve this problem, we can use the Pythagorean theorem in 3D, which involves calculating the hypotenuse of a right-angled triangle in three dimensions.
First, let's find the distance on the ground plane. The airplane moves 12km west and then 10km north, forming a right-angled triangle on the ground. Applying the Pythagorean theorem:
Ground distance = √(12² + 10²) = √(144 + 100) = √244 km
Ground distance ≈ 15.62 km
Now, taking into account the altitude of 5 km, we form another right-angled triangle with the ground distance as one leg and the altitude as the second leg. We apply the Pythagorean theorem again:
Total distance from takeoff point = √(15.62² + 5²)
Total distance = √(243.84 + 25)
Total distance = √268.84 km
Total distance ≈ 16.4 km
Thus, the total distance from the takeoff point is approximately 16.4 km, which is not listed in the provided options, suggesting a potential error in the given answer choices or a misunderstanding in the calculation.