A hill slopes down from a building with a grade of one for to five feet measured along the horizontal (slope of 1/5). If a ladder 36 ft. long is set against the building, with its foot 12ft. down the hill. How high will it reach the building?

To find out how high the ladder will reach the building, we can use the concept of similar triangles. Let's break down the problem step by step.

1. The problem states that the hill has a grade of one for five, which means that for every horizontal distance of 1 foot, the height increases by 5 feet. This forms a right-angled triangle.

2. We are given that the ladder is 36 ft. long and its foot is 12 ft. down the hill. Therefore, the horizontal distance from the foot of the ladder to the building is 36 - 12 = 24 ft.

3. We can set up a proportion to represent the relationship between the height of the ladder and the horizontal distance. Let's call the height of the ladder h ft.
- Height of the ladder / Horizontal distance = Grade of the hill = 1/5
- h / 24 = 1/5

4. To solve for h, we can cross-multiply and then solve for h:
- h = (24 * 1) / 5
- h = 4.8 ft

Therefore, the ladder will reach a height of 4.8 ft on the building.