an airplane is flying 120 km south and 130km west of an airport. It is flying at a height of 10 km . what is the straight line distance to the airport?

the distance z is given by

z^2 = 120^2 + 130^2 + 10^2

To find the straight line distance to the airport, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can imagine a right triangle formed by the airplane's flight path, where the vertical distance is the height of the airplane (10 km), the horizontal distance is the distance traveled west (130 km), and the straight line distance to the airport is the hypotenuse.

Using the Pythagorean theorem,

Hypotenuse^2 = height^2 + distance^2

Hypotenuse^2 = 10^2 + 130^2

Hypotenuse^2 = 100 + 16900

Hypotenuse^2 = 17000

Taking the square root of both sides, we find:

Hypotenuse ≈ √17000

So, the straight line distance to the airport is approximately 130.38 km.