Question

1. Joy wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 105 ft and marks point C. Then she walks 85 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 co-linear.

Answer 1

The answer to your question is below

Explanation:

a) Yes, Joy can conclude that ΔABC is similar to ΔEDC because

∠ACB ≅ ∠ECD they are vertical angles and,

∠ABC ≅ ∠EDC they are right angles

We conclude that ΔABC is similar to ΔEDC because of the AA postulate.

b)
`(AB)/(BC) = (DE)/(CD)`

Solve for AB

AB = (BC)(DE) / (CD)

Substitution

AB = 105 (90) / 85

Simplification

AB = 105(1.06)

Result

AB = 111.2 ft