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(60 points to best answer) (asap please and thank you)
Kayla wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 62 ft and marks point C. Then she walks 93 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are collinear.

Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not?

Suppose (DE) ̅=125 ft. Calculate the distance of (AB) ̅ to the nearest tenth of a foot. Show your work. Don’t forget to label your answer.

60 points to best answer asap please and thank you Kayla wants to find the distance AB across a creek She starts at point B and walks along the edge of the rive class=

Respuesta :

Answer: [tex]83.\overline{3}\text{ feet}[/tex]

Step-by-step explanation:

Since, In the given diagram,

The sides of the triangles ABC and EDC are,

BC = 62 feet, DC = 93 feet and DE = 125 feet(given)

And, angles B and D are right angles,

⇒ [tex] \angle ABC\cong \angle EDC[/tex]

[tex]\text{Also, } \angle ACB\cong \angle ECD[/tex]    ( Vertically opposite angles )

By AA similarity postulate,

[tex]\triangle ABC\sim \triangle EDC[/tex]

The sides of similar triangles are in same proportion ,

⇒  [tex]\frac{AB}{ED}=\frac{BC}{DC}[/tex]

⇒  [tex]AB \times DC = BC \times ED[/tex]

⇒  [tex]AB = \frac{BC.ED}{DC}[/tex]

By substituting the values,

We get,

⇒  [tex]AB = \frac{62\times 125}{93}[/tex]

⇒  [tex]AB = \frac{7750}{93}=83.\overline{3}\text{ feet}[/tex]

dewy32

Answer:

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! smiley

Step-by-step explanation:

'cause it is

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