Angle will be arctan 15/100
=arctan 0.15=8.53 degrees.
=arctan 0.15=8.53 degrees.
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.
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.