Question

(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.

1. 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

Answer 1

Please see below.

Explanation:

Two triangles, whose all angles are equal are called similar and then their corresponding sides are proportional. By corresponding sides, we mean sides opposite equal angles.

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.

(a) Hence, yes triangles are similar

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.