PART 2: A REVIEW OF SLOPE ANGLES Any angle may be expressed as the ratio: rise/run...

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PART 2: A REVIEW OF SLOPE ANGLES Any angle may be expressed as the ratio: rise/run where rise = difference in elevation between two points and run = distance between those two points. Example: if the rise = 20 ft and the run = 50 ft, the slope is 20 ft/50 ft = 0.40. this may also be expressed as a percent grade - a slope of 0.40 is a 40% slope or 40% grade, like you see expressed on road signs in some mountainous areas. The rise/run ratio is the tangent of the slope angle, i.e. tanx = rise/run. So, we can convert the slope angle ratio to degrees by finding the arctangent or tan (using a calculator or trigonomic table). In this case, arctan (0.40) = 21.8. Note that the percent slope is roughly twice the number of degrees. This is a useful rule of thumb. In the diagram to the right, the rise and run are indicated for questions #7-9. 7. Express the slope as a ratio. 8. 9. Calculate the slope in degrees. Express the slope as a percent grade. # 75 ft 10. Suppose you are driving on a mountain highway that crosses the Great Smoky Mountains and see a highway warning sign that says "6% grade, trucks use lower gear". What is a 6% slope when expressed in degrees? PART 2: A REVIEW OF SLOPE ANGLES 7. Ratio: 8. Percent grade: 9. Degrees: 10. Slope angle in degrees (show your work below): PART 2: A REVIEW OF SLOPE ANGLES Any angle may be expressed as the ratio: rise/run where rise = difference in elevation between two points and run = distance between those two points. Example: if the rise = 20 ft and the run = 50 ft, the slope is 20 ft/50 ft = 0.40. this may also be expressed as a percent grade - a slope of 0.40 is a 40% slope or 40% grade, like you see expressed on road signs in some mountainous areas. The rise/run ratio is the tangent of the slope angle, i.e. tanx = rise/run. So, we can convert the slope angle ratio to degrees by finding the arctangent or tan (using a calculator or trigonomic table). In this case, arctan (0.40) = 21.8. Note that the percent slope is roughly twice the number of degrees. This is a useful rule of thumb. In the diagram to the right, the rise and run are indicated for questions #7-9. 7. Express the slope as a ratio. 8. 9. Calculate the slope in degrees. Express the slope as a percent grade. # 75 ft 10. Suppose you are driving on a mountain highway that crosses the Great Smoky Mountains and see a highway warning sign that says "6% grade, trucks use lower gear". What is a 6% slope when expressed in degrees? PART 2: A REVIEW OF SLOPE ANGLES 7. Ratio: 8. Percent grade: 9. Degrees: 10. Slope angle in degrees (show your work below):

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