# 1.4 Summary Problems

1. Using the measurements provided, determine the %slope of the following slopes between Points A and B.

2. On a 60% slope, Todd wants to walk up a slope a distance equivalent to 100 feet horizontal distance. How far should he walk from Point A?

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3. Determine the average slopes between Points A and B on the contour maps below. The scale is 1 inch=2000 feet. The contour interval is 80 feet.

**Answers to Summary Questions**

1. [latex]\displaystyle \left( {\frac{{rise}}{{run}}} \right)\left( {100} \right)=[/latex]%slope

1a. [latex]\left( {\frac{{100ft}}{{90ft}}} \right)\left( {100} \right)=[/latex]111%

1b. [latex]\left( {\frac{{80ft}}{{230ft}}} \right)\left( {100} \right)=[/latex]35%

2. On a 60% slope, we know that the rise is 60% of the run. Therefore, the rise here should be 60 percent of 100 feet or 60 feet. Using the Pythagorean theorem, we can solve for the hypotenuse.

a^{2} + b^{2} = c^{2 } where:

100^{2} + 60^{2} = c^{2}

13,600 = c^{2 }

[latex]\sqrt{{13,600}}=117[/latex]ft.

3. The answers to these questions will depend upon how you measured the horizontal, or map distance, which can be hard to do on a screen. My measurements are shown on the maps below:

At left. Point A is ≈ 3440 feet. Point B is ≈ 3720 feet. The rise is 280 feet. The run is ≈ 2200 feet. Therefore, the average slope is (280)(100)/2200 = 13%.

At right. Point A is ≈ 4040 feet. Point B is ≈ 3280 feet. The rise is 760 feet. The run is 1300 feet. Therefore, the average slope is (760)(100)/2200 = 58%