Example 3-8-14 - Maple Help



Chapter 3: Applications of Differentiation



Section 3.8: Optimization



Example 3.8.14



 • 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.)

 • 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 $B$.

 • Hint: Angles $\mathrm{ABE}$ and $\mathrm{BCF}$ are equal because they are corresponding interior angles of the parallel lines $\mathrm{BE}$ and $\mathrm{CF}$.

 > 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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