Chapter 1.3, Problem 31PPS

To determine

To find the length of trail.

Answer to Problem 31PPS

Length of trail is 4.49 miles.

Explanation of Solution

Given information:

Initial points coordinates: (23,525, 9300)

Final point coordinates: (0, 12,633)

Formula used:

Distance between pair of points= $\sqrt{{(x_2^{}-x_1^{})}^2+{(y_2^{}-y_1^{})}^2}$

Calculation:

Converting into miles,

23,525 feet = 4.45 miles.

9300 feet = 1.76 miles

12,663 feet = 2.39 miles

Now points are X (4.45, 1.76) and Y (0, 2.39) Let the initial point’s coordinates be X and final coordinates be Y .

Now,

  $x_1^{}=4.45,x_2^{}=0$ and, $y_1^{}=1.76,y_2^{}=2.39$

Substituting values,

  $XY=\sqrt{{(4.45-0)}^2+{(2.39-1.76)}^2}$

Solving,

  $XY=\sqrt{{(4.45)}^2+{(0.63)}^2}$

So,

  $XY=\sqrt{19.80+0.39}$

And $XY=\sqrt{20.19}$

Hence, length of trail is 4.49 miles.