Question

An airplane is 275 miles from the airport. To get to its present position, the plane flew 125 miles due south from the airport and then flew due west. To the nearest mile, how far west did the plane fly?

Answer 1

For questions like this, it's better to draw the representation of the problem for us to understand it better. The problem stated that the plane flew 125 miles due south from the airport and then went due west. At the final position of the airplane, it is 275 miles from the airport. The representation of this problem can be drawn as

As you can see, this represents a right triangle and we can solve for the one side of a right triangle using the Pythagorean theorem.

`c^2=a^2+b^2`

C represents the hypotenuse, which is based on the figure it is equal to 275 miles. We let a be 125 miles and b be the unknown. Our working equation to solve b will be

`\begin{gathered} b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}`

Just substitute the values of c and a on the equation above and compute.

`\begin{gathered} b=\sqrt[]{(275)^2-125^2_{}} \\ b=245\text{miles} \end{gathered}`

Hence, the plane traveled 245 miles far west to have the position 275 miles from the airport.