Question

a pole of length l is carried horizontally around a corner where a 2 - ft - wide hallway meets a 9 - ft - wide hallway, as shown in the figure on the right. for 0 < θ < π/2, find the relationship between l and θ at the moment when the pole simultaneously touches both walls and the corner p. estimate θ when l = 15 ft. identify the relationship between l and θ when the pole simultaneously touches both walls and the corner p. choose a. l(θ)=2 sec θ + 9 csc θ b. l(θ)=2 sinθ + 9 cos θ c. l(θ)=2 cos θ + 9 sin θ d. l(θ)=2 csc θ + 9 sec θ

Explanation:

Step1: Use right - triangle relationships

Let the two hallways have widths \(a = 2\) and \(b=9\). If the pole of length \(L\) makes an angle \(\theta\) with the wall of the \(a -\)wide hallway, then the length of the pole can be expressed in terms of \(\theta\) using the sum of the lengths of two segments of the pole in the two hallways. The length of the pole \(L\) is given by \(L(\theta)=2\csc\theta + 9\sec\theta\).

Answer:

D. \(L(\theta)=2\csc\theta + 9\sec\theta\)