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?

Explanation:

Step1: Apply Pythagorean theorem

Let the horizontal distance from the base of the ladder to the wall be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 10\) (length of the ladder) and \(a=9\) (height of the landing). So \(x=\sqrt{c^{2}-a^{2}}=\sqrt{10^{2}-9^{2}}=\sqrt{100 - 81}=\sqrt{19}\approx4.36\) feet.

Step2: Check safety ratio

For a ladder, the safe ratio of height \(h\) to base distance \(b\) is \(4:1\). Here, if \(h = 9\) feet, a safe base distance \(b_{safe}=\frac{9}{4}=2.25\) feet. Since \(4.36>2.25\), the ladder is not in a safe position.

Answer:

Yes