Question

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
Care collinear. She marks point E at this location, as shown.

(a) Can Kayla conclude that AABC and AEDC are similar? Why or why not?
(b) Suppose DE = 54 ft. What is the width of the river? Round to the nearest foot. Provide all work.
d States

Answer 1

Part a) Triangles ABC and CDE are similar by AAA

Part b) The width of the river is 68 feet

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\angle DCE=m\angle ACB ----> by\ vertical\ angles\\m\angle EDC=m\angle CBA----> is\ a\ right\ angle\\m\angle DEC=m\angle CAB----> the\ sum\ of\ the\ internal\ angles\ must\ be\ equal\ to\ 180^o`

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

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

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

`(72)/(90)=(54)/(AB)`

`AB=90(54)/72=68\ ft`