Kayla wants to find the width, AB, of a river. She walks along the edge of the river 90 ft and marks point C. Then she walks 72 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.

Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not? Suppose DE = 54 ft. What is the width of the river? Round to the nearest foot. Provide all work.

Part a: The triangles ∆ABC and ∆EDC are similar by AA similarity rule.

Part b: The width of AB is 67.5 feet

Explanation:

Part a: We need to prove that the two triangles ABC and EDC are similar.

To prove the triangles are similar, then their angles must be similar.

Thus, we have,

∠DCE  and  ∠BCA are similar (vertical angles)

∠CDE  and  ∠CBA are similar (right angles)

∠B and ∠A are similar

Hence, the triangles ∆ABC and ∆EDC are similar by AA similarity rule.

Part b: We need to determine the width of AB

Since, the triangles are similar, then their corresponding lengths are proportional.

Thus, we have,

where , and

Substituting these values, we get,

Multiplying both sides by 90, we get,

Dividing, we have,

Thus, the width of the river AB = 67.5 feet

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice

60.9774

step-by-step explanation:

because when you add 47.6 plus 7.32 equals 54.92

and when you add .0574 + 6= 6.0574

and when you add 54.92 and 6.0574 you get the answer of 60.9774.

plzz mark brainlest last one got deleted. cause i didn't explain it but i did but i understand what the mod meant