A 4:1 (H:V) slope has what grade and slope angle?

To find the grade and slope angle of a 4:1 horizontal to vertical ratio slope, it is essential to understand the definitions involved. The ratio of 4:1 indicates that for every 4 horizontal units traveled, the slope rises 1 vertical unit.

To calculate the slope grade, you can use the formula:

[ Grade (%) = \left( \frac{Vertical Rise}{Horizontal Run} \right) \times 100 ]

Plugging in the values from the ratio:

[ Grade = \left( \frac{1}{4} \right) \times 100 = 25% ]

Next, to find the slope angle, we can use basic trigonometric calculations. The tangent of the angle can be defined as the vertical rise over the horizontal run:

[ \tan(\theta) = \frac{Vertical Rise}{Horizontal Run} = \frac{1}{4} ]

To find the angle, we take the arctangent (inverse tangent) of the rise/run:

[ \theta = \tan^{-1}\left(\frac{1}{4}\right) ]

Using a calculator, the result is approximately 14 degrees.

Therefore, the findings indicate that a 4: