Final answer:
To find the angle a 25-foot ladder makes with the ground when its base is 10 feet from the wall, the tangent function is used; arctan(10/25) results in the angle being approximately 30 degrees.
Step-by-step explanation:
The question involves using trigonometric principles to find the angle a ladder makes with the ground. Given the length of the ladder (25 feet) and the distance from its base to the wall (10 feet), we can use the tangent function to find the angle. To solve for the angle θ, the formula tan(θ) = opposite/adjacent is used, where 'opposite' is the distance from the base of the ladder to the wall, and 'adjacent' is the distance from the ground up the ladder to the wall. In this case:
tan(θ) = 10/25
Using a calculator to find arctan(10/25) will provide the angle θ that the ladder makes with the ground. The correct answer option based on the standard tangent values is D) 30 degrees.