Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right

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Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration.

+3 ft- 4 ft


(a) Show that the length L of the line segment shown as a function of the angle θ is 

L(θ) = 3 sec θ + 4 csc θ 

(b) Graph L = L(θ),0 < θ < π/2. 

(c) For what value of θ is L the least? 

(d) What is the length of the longest ladder that can be carried around the corner? Why is this also the least value of L?

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Precalculus

ISBN: 978-0321716835

9th edition

Authors: Michael Sullivan

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