Question

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 65 ft and marks point C. Then she walks 25 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 Δ and Δ are similar? Why or why not?

(b) Suppose DE = 15 ft. What can Kayla conclude about the width of the river?

Answer 1

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

Part B) The width of the river is about
`39\ ft`

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

In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent

so

m<DCE=m<ACB -----> by vertical angles

m<EDC=m<ABC -----> is a right angle

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

Part B) we know that

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

therefore

`(BC)/(DC)=(AB)/(DE)`

substitute the values and solve for AB

`(65)/(25)=(AB)/(15)`

`AB=15*((65)/(25))=39\ ft`