contestada

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 100ft and marks point C. Then she walks 22ft further and marks point D. She turns 90 degrees 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 triangle ABC and triangle EDC are similar? Why or why not?

(B) Suppose DE = 32ft. What can Kayla conclude about the width of the river? Explain.

Please help?

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

Respuesta :

calculista

Answer:

Part A) The triangles ABC and EDC are similar, because the three internal angles are equal in both triangles

Part B) The width of the river is about [tex]145.45\ ft[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

Part A) we know that

The triangles ABC and EDC are similar, because the three internal angles are equal in both triangles

so

[tex]m<DCE=m<ACB[/tex] -----> by vertical angles

[tex]m<EDC=m<ABC[/tex] -----> is a right angle

[tex]m<DEC=m<CAB[/tex] -----> the sum of the internal angles must be equal to [tex]180[/tex] degrees

Part B) we know that

The triangles ABC and EDC are similar -------> see Part A

therefore

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

substitute the values and solve for AB

[tex]\frac{100}{22}=\frac{AB}{32}[/tex]

[tex]AB=32*(\frac{100}{22})=145.45\ ft[/tex]

aksnkj

A. The two triangles ABC and EDC are similar using AA similarity criterion.

B.  The width of the river is 145.45 ft.

Given information:

Kayla walks along the edge of the river 100ft and marks point C. Then she walks 22ft further and marks point D. She turns 90 degrees and walks until her location, point A, and point C are collinear. She marks point E at this location.

A. The two right triangles ABC and CDE are made.

In the two triangles, angles D and B are equal to 90 degrees.

Also, angle DCE and angle ACB are equal because they are vertically opposite angles.

Using AA similarity rule, triangle ABC is similar to triangle EDC.

B. Suppose DE = 32ft. It is required to calculate the width AB of the river.

The value of AB can be calculated as,

[tex]\dfrac{AB}{DE}=\dfrac{BC}{CD}\\\dfrac{AB}{32}=\dfrac{100}{22}\\AB=145.45\rm\; ft[/tex]

Therefore, the width of the river is 145.45 ft.

For more details, refer to the link:

https://brainly.com/question/24583211

Otras preguntas