A hill that has a 15 % grade is one that rises 15.0 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?
Angle will be arctan 15/100
=arctan 0.15=8.53 degrees.
To find the angle at which the hill is inclined above the horizontal, you can use trigonometry. The grade of the hill is given as a percentage, which represents the ratio of the vertical rise to the horizontal distance.
The formula to find the angle of inclination is:
Angle = arctan(Grade)
In this case, the grade is 15%. Converting this to a decimal, the grade would be 0.15. Therefore, the formula becomes:
Angle = arctan(0.15)
Using a calculator, you can find the angle to be approximately 8.53 degrees.
So, a hill with a 15% grade is inclined approximately 8.53 degrees above the horizontal.
To find the angle by which the hill is inclined above the horizontal, we can use the trigonometric tangent function. The tangent of an angle is equal to the ratio of the vertical rise to the horizontal distance.
In this case, the tangent of the angle θ is equal to 15.0 m (the vertical rise) divided by 100.0 m (the horizontal distance). Therefore, we have:
tan(θ) = 15.0 / 100.0
To find the angle θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(15.0 / 100.0)
Using a calculator or mathematical software, we can calculate the inverse tangent of 15.0 / 100.0 to find the angle:
θ ≈ 8.53 degrees
Therefore, the hill is inclined approximately 8.53 degrees above the horizontal.