Question

to access a landing that is nine feet above the adjacent floor, a worker climbs an unsecured 10-foot ladder that has slip-resistant feet. does this ladder pose a fall hazard to the worker? select the best option. yes no

Explanation:

Step1: Analyze the right triangle

We can model this situation as a right triangle, where the ladder is the hypotenuse (\(c = 10\) feet), the height of the landing is one leg (\(a = 9\) feet), and the distance from the base of the ladder to the wall is the other leg (\(b\)). We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) to find \(b\).
Rearranging for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).
Substituting the values, \(b = \sqrt{10^{2}-9^{2}}=\sqrt{100 - 81}=\sqrt{19}\approx4.36\) feet.

Step2: Check the ladder angle safety

A safe ladder angle (angle between the ladder and the ground) typically has the base of the ladder about \(\frac{1}{4}\) of the ladder's height from the wall. For a 10 - foot ladder, the recommended base distance is \(\frac{10}{4}=2.5\) feet. Our calculated \(b\approx4.36\) feet is greater than 2.5 feet, meaning the ladder is too far from the wall, making it unstable and posing a fall hazard.

Answer:

Yes