Question

THE ANSWER IS NOT 30.09 or 2.17. PLEASE HURRY ND PLEASE HELP ME!

A plane, 50 miles away from its destination, is flying toward the airport at an altitude of 30,500 feet. Later, this same plane is 20 miles from the airport and has descended to an altitude of 18,000 ft.
How far has the plane flown?

Answer 1

In feet:
`\boxed{158,892 \textrm{ feet}}`

In miles:
`\boxed{\textrm{ 3.11 \;miles}}`

Explanation:

A diagram really helps here and so I have drawn one for your understanding

From the diagram we see that Point A refers to the location of the plane when it is 50 miles away from the airport at am altitude of 30,500 feet

In a 2D coordinate system where x refers to the horizontal distance from the airport value and y refers to the altitude,
=> Point A has coordinates (50, 30500)

When the plane is 20 miles away from the airport, the altitude has dropped down to 18000 feet

This location is represented as point B(20, 18000)

The horizontal distance traveled by the plane is 50 - 20 = 30 miles

The vertical distance traveled by the plane(drop in altitude) is 30,500 - 18,000 = 12, 500

These two form the legs of a right triangle with the actual path of descent as the hypotenuse of the right triangle (see figure)

The distance c traveled by the plane is the distance from Point A to Point B which can be computed using the Pythagorean theorem given the two legs of the right triangle

The general formula is :


`\mbox{\large c = \sqrt{a^(2) + b^(2)}}`

where c is the length of the hypotenuse, a and b are the lengths of the other two sides

We have a = 12, 500 feet and b = 30 miles

Convert miles to feet to get same units:

a = 12, 500 feet

b = 30 miles = 30 x 5280 feet = 158400

`\mathbox{ c = \sqrt{158400^(2) + 12500^(2)}}`

`c = √(25090560000 + 156250000)`

`c = √(25246810000)`


`\mathrm{c = 158,892.45 \;feet}\\`

`\mathbox{ \textrm{c = 158,892 feet (to the nearest foot)}}`

So the distance traveled by the plane is 158, 992 feet (to the nearest foot)

This works out to 158992/5280 miles = 30.11 miles which is pretty close to 3.09

Maybe you are required to answer in feet and not in miles.

I don't know