Question

You start driving north for 63 miles, turn right, and drive east for another 16 miles.

Answer 1

You must travel 65 miles to return directly back to your starting point

Solution:

Given that you start driving north for 63 miles, turn right, and drive east for another 16 miles.

Hence we can say that, you have traveled in form of right angled triangle where the vertical leg is 63 miles and horizontal leg is 16 miles

The route you travel to get back to starting point is the hypotenuse

The reference figure for right angled triangle is attached below

BC = length of hypotenuse

AB = length of vertical leg of right angled triangle

AC = length of horizontal leg of right angled triangle

Let from the figure AB = 63 miles,  

Then I turned right and drive east for another 16 miles

So, let AC = 16 miles

Now, To reach directly back to the starting point,  

The amount of distanced to be traveled back to starting point is BC

Which can be calculated using Pythagoras theorem

The Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, we get

$\begin{array}{l}{\mathrm{BC}^{2}=\mathrm{AB}^{2}+\mathrm{BC}^{2}} \\\\ {\mathrm{BC}^{2}=(63)^{2}+(16)^{2}} \\\\ {\mathrm{BC}^{2}=3969+256} \\\\ {\mathrm{BC}^{2}=4225}\end{array}$

$B C=\sqrt{4225}$

BC = 65 miles

Hence , the distanced to be traveled back to your starting point is 65 miles