Working with Scale

Table of Contents

  1. Working with Scale
  2. Measuring Distance Using a Graphic Scale
  3. Calculating Slope When Determining Distance
  4. Converting Map Distance to Ground Distance Using a Representative Fraction (RF)
  5. Determining Scale Using a Representative Fraction

Calculating Slope When Determining Distance

In the previous example, a line was drawn between point A and point B on the Arcata North USGS Topographic Quadrangle. You were asked to estimate the distance between these two points using a graphic scale bar. However, the distances measured do not factor changes in elevation. In this step, you will use the Pythagorean Theorem to calculate the slope distance.

To review concepts related to the Pythagorean Theorem, watch the following video by Khan Academy.



An image of the Pythagorean theorem.
If you will recall, the Pythagorean Theorem measures the hypotenuse of a triangle, where C is the distance along the slope.

Let us assume that Point A on the map is at an elevation of 90 feet above sea level. Let us also assume the point B on the map is 680 feet above sea level. Last, for our purposes here, assume that there are a gradual rise and constant slope between the two points on the map.


On a separate piece of paper, write down the answers to the following question:

An image of the Arcata North USGS Topographic Quadrangle.
The purple line over the Feet scale bar is the approximate distance between point A and B. Click to view the image in a larger size.
  1. Using your answer from Question 4 and the Pythagorean Theorem, what is the approximate distance in feet between points A and B on the map given the changes in elevation?