# 1.4: Summary Problems

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- 20246

## 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. On the contour maps below, determine the average slopes between Points A and B. The scale is 1”=2000’. The contour interval is 80’.

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**Answers to Summary Questions**

1. %slope

1a. 111%

1b. 35%

2. On a 60% slope, we know that the rise is 60% of the run. Therefore, the rise here should be 60% 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 }

ft.

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

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

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