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?

Question

Mathematics

Killian Black

Today, 10:11

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?

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Answers (1)

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Theodore Rubio · Answer 1

Let x = length of pipe.

Use Law of Cosines to find x: x^2 = 7^2 + 12^2 - 2 (7) (12) cos (56.4) = 98.03; x=9.901.

Let y = angle between pipe and ground.

Use Law of Sines to calculate y.

sin y/12 = sin (56.4) / 9.901; sin y = 1 (approx). y = 90 deg.

Answer: 90 deg.