Algebra

We can use the tangent ratio which is equal to the opposite side divided by the adjacent side. So, the opposite side (the distance from the ladder to the building) is 10 feet (120 inches). We need to solve for the adjacent side, which is the distance from the base of the ladder to the level ground. tan(72°) = opposite/adjacent 120/adjacent = tan(72°) adjacent = 120/tan(72°) ≈ 83.6 inches Therefore, the base of the ladder should be placed 83.6 inches away from the side of the building. To find the distance up the side of the building the ladder will reach, we use the Pythagorean theorem. Using the 10-foot opposite side, and the 83.6 inch adjacent side, we can calculate the hypotenuse as follows: Hypotenuse^2 = Opposite^2 + Adjacent^2 Hypotenuse^2 = (10 ft)^2 + (83.6)^2 Hypotenuse ≈ 12.4 ft Therefore, the ladder will reach 12.4 feet up the side of the building.