Question

An airplane covered 21 miles of its route while decreasing its altitude by 46,000 feet. How do you find the slope of the airplane's line of descent?

Answer 1

`.41486291486...`

Explanation:

Think of the problem as a right triangle.

The airplane has traveled `21` miles of its distance, which is along the `x`-axis. Thus, the horizontal line has a length of `21` miles. But, you want to convert this to feet, as the other given unit is in feet.

`21 * 5280 = 110880` feet

The airplane has also dropped `46000` feet. This can be represented as a vertical line with a length of `46000` feet.

We now have the total change in `x` (`110880` feet) and the total change in `y` (`46000` feet).

The airplane's line of descent is the hypotenuse of the two lines we determined.

To calculate the slope of this line, simply use the idea of `(rise)/(run)`, or `(Delta y)/(Delta x)`. We know both values, so we can calculate the slope.

Slope of hypotenuse = slope of airplane's line of descent =

`46000/110880`

= `.41486291486...`