A ladder leans against a building. The top of the ladder touches the building 10 feet above the ground. The foot of the ladder is 4 feet from the building. Find the angle that the ladder makes with the level ground.

To find the angle that the ladder makes with the level ground, we can use trigonometry, specifically the tangent function. Here's how you can approach the problem step by step:

1. Draw a right triangle representing the situation described. The ladder forms the hypotenuse, the distance from the building to the foot of the ladder is the adjacent side, and the height where the ladder touches the building is the opposite side.

2. Given that the ladder touches the building 10 feet above the ground and the foot of the ladder is 4 feet from the building, we have the opposite side as 10 ft and the adjacent side as 4 ft.

3. Now, use the tangent function which is defined as the ratio of the opposite side to the adjacent side in a right triangle. The formula is: tan(θ) = opposite/adjacent.

4. Substitute the values we have into the formula: tan(θ) = 10/4 = 5/2.

5. To find the angle θ, we need to take the arctan (inverse tangent) of 5/2. This gives us θ ≈ 68.2 degrees.