Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration. It can be shown that the length L of the ladder as a function of θ is L(θ) = 4 csc θ + 3sec θ.

(a) In calculus, you will be asked to find the length of the longest ladder that can turn the corner by solving the equation

3sec θ tan θ -4csc θ cot θ = 0, 0° < 0 < 90°

Solve this equation for θ.

 

(b) What is the length of the longest ladder that can be carried around the corner?

(c) Graph L = L(θ),0° ≤ 0 ≤ 90°, and find the angle θ that minimizes the length L.

(d) Compare the result with the one found in part (b). Explain why the two answers are the same.

Transcribed Image Text:

- 3 3 ft→ 4 ft