What is the vertical distance in a 3:1 trench if it reaches 36 feet horizontally?

To determine the vertical distance in a 3:1 trench that extends 36 feet horizontally, one must first understand what a 3:1 slope represents. In a 3:1 slope, for every 3 units of horizontal distance, there is a corresponding vertical rise of 1 unit. This means that for every 3 feet of horizontal movement, the trench rises 1 foot.

Given a horizontal distance of 36 feet, you can establish the relationship by dividing the horizontal distance by 3 to find the vertical rise.

Calculation:

• Horizontal distance: 36 feet

• Since the slope ratio is 3:1, you divide the horizontal distance by 3:

[

\text{Vertical distance} = \frac{36 \text{ feet}}{3} = 12 \text{ feet}

]

Thus, the vertical distance of the trench at this horizontal distance is 12 feet. Understanding this ratio is crucial in excavation and grading as it ensures safety and structural integrity in trench designs.