Example 3-8-14 - Maple Help
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Chapter 3: Applications of Differentiation

Section 3.8: Optimization

Example 3.8.14

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Find the length of the longest ladder that can be carried horizontally around the corner of the passageway shown in Figure 3.8.14(a). (The horizontal and vertical segments, corridors of widths b and a, respectively, are at right angles to each other.)

 

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Hint: The longest ladder that can be carried around the corner at point B is the shortest line segment from A to C that also passes through B.

 

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Hint: Angles ABE and BCF are equal because they are corresponding interior angles of the parallel lines BE and CF.

p1:=plot([[0,0],[0,5],[6,5]],style=line,color=black):
p2:=plot([[2,0],[2,13/5],[6,13/5]],style=line,color=black):
p3:=plot([[[0,1],[2,1]],[[5,13/5],[5,5]]],style=line,linestyle=dot,color=red):
p4:=plot([[0,1],[5,5]],style=line,color=green):
p5:=plots:-textplot({[-.2,1,typeset(A)],[1.9,2.8,typeset(B)],[5,5.2,typeset(C)],[5,12/5,typeset(F)],[2.2,1,typeset(E)]},font=[default,bold,12]):
p6:=plots:-textplot({[1.8,2.2,typeset(theta)],[4.8,4.6,typeset(theta)]},font=[default,12]):
p7:=plots:-textplot({[1,.8,typeset(a)],[5.2,3.7,typeset(b)]},font=[default,12]):
plots:-display(p||(1..7),scaling=constrained,view=[-.5..6,0..5.2],axes=none);

 

Figure 3.8.14(a)   Ladder in right-angled corridor

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