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

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Multiple Choice

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

To determine the grade and slope angle of a 4:1 (H:V) slope, it's important to understand what the ratio represents. The ratio indicates that for every 4 horizontal units (H), there is a rise of 1 vertical unit (V). First, let's calculate the grade. The formula for calculating the grade of a slope is: \[ \text{Grade} = \left(\frac{\text{Vertical Rise}}{\text{Horizontal Run}}\right) \times 100\% \] Substituting the values from the 4:1 slope: \[ \text{Grade} = \left(\frac{1}{4}\right) \times 100\% = 25\% \] Next, to find the slope angle, we use the tangent function, which is defined as the ratio of the vertical rise to the horizontal run: \[ \tan(\theta) = \frac{1}{4} \] To find the angle, we can take the arctangent (inverse tangent) of 1/4: \[ \theta = \arctan\left(\frac{1}{4}\right) \] Using a calculator or trigonometric tables

To determine the grade and slope angle of a 4:1 (H:V) slope, it's important to understand what the ratio represents. The ratio indicates that for every 4 horizontal units (H), there is a rise of 1 vertical unit (V).

First, let's calculate the grade. The formula for calculating the grade of a slope is:

[

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

]

Substituting the values from the 4:1 slope:

[

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

]

Next, to find the slope angle, we use the tangent function, which is defined as the ratio of the vertical rise to the horizontal run:

[

\tan(\theta) = \frac{1}{4}

]

To find the angle, we can take the arctangent (inverse tangent) of 1/4:

[

\theta = \arctan\left(\frac{1}{4}\right)

]

Using a calculator or trigonometric tables

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