Question

Please Help! I'm having a lot of trouble with this question!!!

Kayla wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 62 ft and marks point C. Then she walks 93 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are collinear.


(a) Can Kayla conclude that ∆ABC and ∆EDC are similar? Why or why not?


(b) Suppose (DE) ̅=125 ft. Calculate the distance of (AB) ̅ to the nearest tenth of a foot. Show your work. Don’t forget to label your answer.

Answer 1

a ∆ABC and ∆EDC are similar

b. AB = 83.3 ft

Explanation:

a. We need to determine if ∆ABC and ∆EDC are similar.

We know B = D = 90

We know C = C because they are vertical angles and vertical angles are equal

Therefore A = E because they are triangles, and if 2 angles in a triangle are equal the third angles must be equal.

∆ABC and ∆EDC are similar

b. We know that because they are similar triangles

AB BC

------ = ---------

ED DC

Substituting in

AB 62

------ = ---------

125 93

Using cross products

93 AB = 62*125

93 AB = 7750

Divide by 93

AB = 7750/93

AB = 83.3333333333(repeating)

Rounding to the nearest tenth ft

AB = 83.3 ft