Question

If an airplane passes directly over your head at an altitude of 12 kilometers, how far is the airplane from your position after it has flown 16 kilometers farther at the same altitude?

Answer 1

The final distance between your position and the airplane after it has flown 16 kilometers farther at the same altitude is approximately 20 kilometers.

Step-by-step explanation:

To find the distance between your position and the airplane after it has flown 16 kilometers farther, you can use the Pythagorean theorem. The altitude of the airplane remains constant at 12 kilometers, so we can create a right triangle with one leg representing the original distance from your position to the plane and the other leg representing the additional 16 kilometers flown. The hypotenuse of this triangle represents the final distance between your position and the airplane. Using the theorem, the final distance can be calculated as:

distance^2 = (original distance)^2 + (additional distance)^2

Plugging in the values, we have:

distance^2 = (12km)^2 + (16km)^2

Simplifying, we get:

distance^2 = 144km^2 + 256km^2

distance^2 = 400km^2

Taking the square root of both sides, we find that the final distance between your position and the airplane is approximately 20 kilometers.

Answer 2

20 kilometres

Step-by-step explanation:

We will imagine a triangle. The hypotenuse of the triangle is the distance between you and the plane. 16 kilometres is the aerial space between you two, in other words its the base of the triangle. 12 km is the length of the third leg of the triangle. We will apply the pythagorean theorem to find the length of the hypotenuse and the distance between you and the plane.

a^2 + b^2 = c^2

12^2 + 16^2 = c^2

144 + 256 = c^2

400 = c^2

square root of 400 is c which equals 20 km.