+3 ft 4 ft (a) Show that the length L of the ladder shown as a function of the angle 0 is L(0) = 3 sec 0 + 4 csc 0 (b) Graph L = L(0),0 < 0 < (c) For what value of 0 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? 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 53E
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Carrying a Ladder around a Corner 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 ladder shown as a function
of the angle 0 is
L(0) = 3 sec 0 + 4 csc 0
(b) Graph L = L(0),0 < 0 <
(c) For what value of 0 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?
2
Transcribed Image Text:+3 ft 4 ft (a) Show that the length L of the ladder shown as a function of the angle 0 is L(0) = 3 sec 0 + 4 csc 0 (b) Graph L = L(0),0 < 0 < (c) For what value of 0 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? 2
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