Question

(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 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.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer

Answer 1

Step-by-step explanation

Part a)

We know that two triangles are similar if two pairs of corresponding angles are equal.

In this case, we have:

• Angles EDC and ABC are right angles. Then, these angles are equal.

,

• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.

Answer

Since the above condition is fulfilled, triangles ABC and EDC are similar.

Part b)

When two triangles are similar, their corresponding sides are in the same ratio.

`(a)/(e)=(b)/(d)=(c)/(c^(\prime))`

Then, we can write and solve the following equation:

`\begin{gathered} (300ft)/(80ft)=(c)/(50ft) \\ 3.75=(c)/(50ft) \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=(c)/(50ft)*50ft \\ 187.5ft=c \end{gathered}`Answer

The width of the river is 187.5 feet.