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Michelle wants to find the width, AB, of a river. She walks along the edge of the river 100 ft and marks point C.Then she walks 22 ft further and marks point D. She turns 90° and walks until her location, points A, and point C are collinear. She marks point E at this location, as shown.(a) Can Kayla conclude that △ and △ are similar? Why or why not?(b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain

Michelle wants to find the width AB of a river She walks along the edge of the river 100 ft and marks point CThen she walks 22 ft further and marks point D She class=

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Solution

Question A:

- Two triangles are similar if all the 3 angles within the triangles are equal.

- Triangles ABC and EDC are similar because:

1. Both triangles have right-angles.

2. 3. Since 2 angles are the same for both triangles, then the third angle must be the same.

- Thus, the 2 triangles are similar

Question B:

- Given that DE = 32ft, we can find the length of AB using similar triangles:

[tex]\begin{gathered} \frac{DE}{DC}=\frac{AB}{CB} \\ \\ \frac{32}{22}=\frac{AB}{100} \\ \\ \therefore AB=32\times\frac{100}{22} \\ \\ AB=145.\overline{45} \end{gathered}[/tex]

- Thus, the width of the river is 145.4545... ft

Final Answer

The width of the river AB is 145.4545... ft

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