Question

Please Help

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

Answer:

Part a) Triangles ABC and CDE are similar by AAA

Part b) The width of the river is $39\ ft$

Step-by-step explanation:

Part a)

we know that

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

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

so

$m<DCE=m<ACB$

$m<EDC=m<CBA$

$m<DEC=m<CAB$

Part b)

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

so

$\frac{DC}{CB}=\frac{DE}{AB}$

substitute the values and solve for AB (the width of the river)

$\frac{25}{65}=\frac{15}{AB}$

$AB=15*65/25=39\ ft$