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1.Kayla 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, point 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.

(a) No, because ABC and EDC are right triangles but have different length of bases.

(b) 145.45 ft

22/100=32/x    =145.45

KennedyPape  Jan 23, 2018

#1
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(a)

Remember, similar triangles can have different side lengths.

In order for two triangles to be similar, the angles must be the same.

Since  ∠DCE  and  ∠BCA  are vertical angles, they have the same measure.

Since  ∠CDE  and  ∠CBA  are right angles, they have the same measure.

And since two of the angles are the same, the third angle must be the same,

so  △ABC is similar to △EDC  by the Angle-Angle similarity rule.

(b)

To solve this, we have to know that △ABC is similar to △EDC .

Because △ABC is similar to △EDC , we can say that

22/100  =  32/x   , where  x  is the length of  AB  in feet.

x  =  3200/22   ≈   145.45

So the width of the river is about  145.45  feet, just as you found!

hectictar  Jan 23, 2018
Sort:

#1
+6939
+3

(a)

Remember, similar triangles can have different side lengths.

In order for two triangles to be similar, the angles must be the same.

Since  ∠DCE  and  ∠BCA  are vertical angles, they have the same measure.

Since  ∠CDE  and  ∠CBA  are right angles, they have the same measure.

And since two of the angles are the same, the third angle must be the same,

so  △ABC is similar to △EDC  by the Angle-Angle similarity rule.

(b)

To solve this, we have to know that △ABC is similar to △EDC .

Because △ABC is similar to △EDC , we can say that

22/100  =  32/x   , where  x  is the length of  AB  in feet.

x  =  3200/22   ≈   145.45

So the width of the river is about  145.45  feet, just as you found!

hectictar  Jan 23, 2018

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