What is the horizontal distance in a trench with a slope of 3:1 and a vertical distance of 12 feet?

To determine the horizontal distance in a trench with a slope of 3:1 and a vertical distance of 12 feet, it’s important to understand what the slope ratio refers to. A slope of 3:1 means that for every 3 feet of horizontal distance, there is a corresponding 1 foot of vertical rise.

Given the vertical distance of 12 feet, you can calculate the horizontal distance by multiplying the vertical distance by the horizontal component of the slope ratio. Since the vertical distance creates a triangle with a vertical leg of 12 feet and a horizontal leg determined by the slope, you would multiply 12 feet by the horizontal ratio in the slope.

In this case, for every 1 foot of vertical distance, there are 3 feet of horizontal distance. Thus, for 12 feet of vertical distance, the calculation is:

Horizontal distance = Vertical distance × 3

Horizontal distance = 12 feet × 3 = 36 feet

This calculation confirms that the correct horizontal distance in the trench is indeed 36 feet. Understanding slope ratios is crucial for applications in excavation and grading, as it directly impacts the safety and design of the slopes.