I made a diagram from your description.
Notice that booth ∠ACB and ∠DCE are vertical angles, and we know that vertical angles are congruent by the vertical angles theorem. Also, since she turned around 90° from B towars D and from D towards E, ∠ABC and ∠CDE are right angles, and we also know that right triangles are congruent.
So far we prove that ∠ACB≅∠DCE and ∠ABC≅∠CDE, and since both angles are corresponding congruent angles, we just prove that △ABC and △EDC are similar by the AA postulate.
The corresponding sides we are interested in are AB, BC, ED, and DC:
[tex] \frac{AB}{BC} = \frac{ED}{DC} [/tex]
[tex] \frac{AB}{79} = \frac{57}{23} [/tex]
Now the only thing is cross multiply and divide to find the length of AB:
[tex]AB= \frac{(57)(79)}{23} =195.87[/tex]
We can conclude that the distance from A to B to the nearest whole foot is 196 feet.
