(a) Can Kayla conclude that and are similar? Why or why not?
(b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain.

Question

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 22 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.

NEED HELP PLEASE

Mason Adams · Accepted Answer

Please see below.

When two triangles have equal angles throughout, they are said to be similar, and their corresponding sides—that is, the sides that are opposite equal angles—are then said to be proportionate. Further observe that if two angles of a triangle are equal to two angles of other triangle, then remaining third angles are equal too, as sum of angles of atriangle is always #180^@#. In given figure we have two triangles #DeltaABC# and #DeltaCDE#. In these triangles we have #m/_ABC=m/_CDE=90^@# #m/_ACB=m/_DCE# - as they are vertically opposite angles. then #m/_CAB=m/_CED# as they are remaining angles. Therefore, triangles are similar, yes. This means #(AB)/(DE)=(BC)/(CD)# .................(A) Observe that #AB# and #DE# are opposite equal angles #m/_ABC# and #m/_CDE# and #BC# and #CD# are opposite equal angles #m/_CAB# and #m/_CED#. (b) As #DE=32# feet, (A) gives us #(AB)/32=100/22# i.e. #AB=100/22xx32=145.45# feet.

(a) Can Kayla conclude that and are similar? Why or why not? (b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain.