A hill that has a 31.4 % grade is one that rises 31.4 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?

arctan (.314)=?

Tan(b)=31.4 /100

To find the angle of inclination of a hill given its grade, you can use trigonometry. In this case, the grade of the hill is given as a percentage, which represents the ratio of the rise (vertical distance) to the run (horizontal distance).

The formula to calculate the angle of inclination is:

Angle of inclination = arctan(grade)

Step 1: Convert the grade percentage to a decimal.
In this case, the grade is given as 31.4%. To convert it to a decimal, divide it by 100:

Grade = 31.4% / 100 = 0.314

Step 2: Apply the arctan function to find the angle.

Angle of inclination = arctan(0.314)

Using a scientific calculator or a function lookup, you can find that the arctan(0.314) is approximately 17.2 degrees.

Therefore, a hill with a 31.4% grade is inclined at an angle of approximately 17.2 degrees above the horizontal.