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 when it extends horizontally by 36 feet, it's important to understand what a 3:1 slope means. A 3:1 slope indicates that for every 3 horizontal units, there is a 1 vertical unit of change.

In practical terms, with a 3:1 slope, you can visualize that for every 3 feet of horizontal distance, you rise or fall by 1 foot vertically. So, if you have a horizontal distance of 36 feet, you can break that down into segments of 3 feet:

1. Divide the total horizontal distance by the horizontal distance represented in the slope:

( 36 feet \div 3 = 12 ).

2. This means that there are 12 segments of 3 feet in the 36 feet. Since each segment corresponds to a vertical distance of 1 foot, you multiply the number of segments by the vertical change of each segment:

( 12 \times 1 foot = 12 feet ).

Thus, the trench will have a vertical distance of 12 feet when it extends 36 feet horizontally, validating the correct choice.