What is the distance from the wall to the foot of a ladder, expressed as a fraction of the ladder's length?

What is the distance from the wall to the foot of a ladder, expressed as a fraction of the ladder's length?

• A. One quarter of the ladder length
• B. One half of the ladder length
• C. One quarter of the wall height
• D. One foot

Answer: (A)

A stable ladder setup uses a base distance from the wall that’s about one-quarter of the ladder’s length. If the ladder length is L, the horizontal distance from the wall is x = L/4. The ladder, wall, and ground form a right triangle with the ladder as the hypotenuse. By the Pythagorean theorem, the vertical reach is h = sqrt(L^2 − x^2) = sqrt(L^2 − L^2/16) = (L/4)√15. The angle between the ladder and the ground then has tangent h/x = √15, which is about 3.873, giving an angle of roughly 75.96 degrees—this is the commonly recommended ladder angle. So the distance, as a fraction of the ladder length, is one quarter.

A stable ladder setup uses a base distance from the wall that’s about one-quarter of the ladder’s length. If the ladder length is L, the horizontal distance from the wall is x = L/4. The ladder, wall, and ground form a right triangle with the ladder as the hypotenuse. By the Pythagorean theorem, the vertical reach is h = sqrt(L^2 − x^2) = sqrt(L^2 − L^2/16) = (L/4)√15. The angle between the ladder and the ground then has tangent h/x = √15, which is about 3.873, giving an angle of roughly 75.96 degrees—this is the commonly recommended ladder angle. So the distance, as a fraction of the ladder length, is one quarter.