Question

(GEOMETRY 100 POINTS)
Kayla wants to find the width, AB, of a river. She walks along the edge of the river 75 ft and marks point C. Then she walks 35 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 = 21 ft. What can Kayla conclude about the width of the river?

PLEASE SHOW YOUR WORK, PLEASE I NEED HELP

Answer 1

Answer:

Part A) Yes, Kayla can conclude that the triangles ABC and EDC are similar (see the explanation)

Part B) The width of the river is 45 feet

Step-by-step explanation:

The correct question is

(A) Can Kayla conclude that ΔABC and ΔEDC are similar? Why or why not?

(B) Suppose DE = 21 ft. What can Kayla conclude about the width of the river?

The picture in the attached figure

we know that

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

Part A) we know that

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar

In this problem

$m\angle DCE=m\angle ACB$ -----> by vertical angles  

$m\angle EDC=m\angle ABC$ -----> is a right angle

therefore

Triangles ABC and EDC are similar by AA Similarity Theorem

Part B) we know that

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

so

$\frac{BC}{DC}=\frac{AB}{ED}$

substitute the given values and solve for AB

$\frac{75}{35}=\frac{AB}{21}$

$AB=\frac{75}{35}(21)$

$AB=45\ ft$

therefore

The width of the river is 45 feet

Answer 2

Answer:

1) They are similar

2) 45 ft

Step-by-step explanation:

1) similar because both triangles have congruent interior angles

2) 75/35 = AB/21

AB = 45 ft