Chapter 15, Problem 17P

The length of the longest ladder that can negotiate the corner depicted in Fig. P15.17 can be determined by computing the value of $\theta$ that minimizes the following function:

$L\left(\theta \right)=\frac{w_1}{\sin \theta }+\frac{w_2}{\sin \left(\pi -\alpha -\theta \right)}$

For the case where $w_1=w_2=2\text{m}$, use a numerical method (including software) to develop a plot of L versus a range of $\alpha$'s from $45°\text{to 135}°$.

FIGURE P15.17

A ladder negotiating a corner formed by two hallways.