# 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?

Nov 6, 2015

$.41486291486 \ldots$

#### 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.

$21 \cdot 5280 = 110880$ 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 $\frac{r i s e}{r u n}$, or $\frac{\Delta y}{\Delta x}$. We know both values, so we can calculate the slope.

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

$\frac{46000}{110880}$

= $.41486291486 \ldots$