The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. The top of the ladder is placed an unknown distance off the ground, leaning on the pipe. The ladder and the ground meet at a 56.4° angle. At what angle does the pipe meet the ground?

The ladder’s top is 12 sin(56.4°) ≈ 10.0 feet above the ground, and its horizontal distance from the ladder’s bottom is 12 cos(56.4°) ≈ 6.63 feet. Since the pipe’s base is 7 feet from the ladder’s bottom, the top is about 7 − 6.63 = 0.37 feet horizontally from the pipe’s base. Thus the pipe’s angle with the ground is arctan(10.0 ÷ 0.37) ≈ 88°, so the closest choice is 88.2°.

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