Chapter 10.1, Problem 15P

A pilot flies a plane south and then 600 miles west, where she lands the plane. How far south did the pilot fly the plane if she lands 610 miles from her starting point?

To determine

To find the distance travelled by the pilot towards south.

Answer to Problem 15P

The pilot travelled $110$ miles south.

Explanation of Solution

Given information:

The given statement is:

“A pilot flies a plane south and then $600$ miles west, where she lands the plane. How far south did the pilot fly if she lands $610$ miles from her starting point?”

Formula used:

The following formula is used:

  ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

Calculation:

The solution can be obtained by:

  $\begin{array}{l}{c}^2=a^2+b^2\left[\text{Pythagoras theorem}\right]\\ {610}^2=a^2+{600}^2\left[\text{Substitute the values}\right]\\ a^2=372100-360000\\ a=\sqrt{12100}\left[\text{Square root of both sides}\right]\\ c=110\end{array}$

Hence, the pilot travelled $110$ miles south.