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

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.

try soting them out first

step-by-step explanation: