For a 24-foot ladder at the proper 75-degree angle, approximately how far should the base be from the wall?

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Multiple Choice

For a 24-foot ladder at the proper 75-degree angle, approximately how far should the base be from the wall?

Explanation:
When a ladder leans at 75 degrees, the ladder length acts as the hypotenuse of a right triangle formed by the wall and the ground. The distance from the wall to the base is the side adjacent to that angle, so it equals the hypotenuse times the cosine of the angle. Compute 24 ft × cos(75°) ≈ 24 × 0.2588 ≈ 6.2 ft, which is about 6 feet. So the base should be roughly 6 feet from the wall. If you used 12, 4, or 8 feet, you’d be matching different angles (not 75°), which is why those distances don’t fit.

When a ladder leans at 75 degrees, the ladder length acts as the hypotenuse of a right triangle formed by the wall and the ground. The distance from the wall to the base is the side adjacent to that angle, so it equals the hypotenuse times the cosine of the angle. Compute 24 ft × cos(75°) ≈ 24 × 0.2588 ≈ 6.2 ft, which is about 6 feet. So the base should be roughly 6 feet from the wall. If you used 12, 4, or 8 feet, you’d be matching different angles (not 75°), which is why those distances don’t fit.

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