I sadly never got the chance to solve these kind of things using English terminology, so please try to bear with my poor quality, sloppy, subpar explanation.
First you prove that ∠DBC = ∠EBA since AC crosses ED. Then you prove that △DBC and △EBA are similar as ∠DBC = ∠EBA, ∠CDB = ∠AEB and EB (1400ft.) is proportional to BD (700ft.). Finally, as △DBC and △EBA are similar, that means that DC is proportional to AE by the same ratio as EB is to BD. Which gives us:
@phoinexflame seems to have a good explanation.
Definitions quoted from quick googling.
What I learned as X angles.
“When two lines intersect, the opposite (X) angles are equal”
Similar shapes topic. “Having the same shape; having corresponding sides proportional and corresponding angles equal”.
Here you are trying to match equal angles as pairs.
∠DBC = ∠EBA : Explained by X angles
∠CDB = ∠AEB : Fact given in question
You could also say
∠BCD = ∠EAB : If you know 2 angles of a triangle you effectively know the third angle of a triangle. (All 3 angles of a triangle add to 180 degrees.)
Practically since the triangles are similar, one triangle is the same shape as the other by scaled to a different size. If something is scaled, everything is enlarged (or shrinked) to a fixed ratio.
Like how you can match angles as pairs, you can match corresponding sides of a shape.
AB & BC (BC unknown)
EB & BD (both known values)
x (AE) & DC (x unknown)
Then you just solve stuff using ratios.
(The scaling factor)
x / DC = EB / BD
You also should be careful not to get points deducted from not writing units .
So write the answer as x = 1600 ft.
If you google “similar shapes” you can probably find something.
I did honestly think about mentioning you, but I didn’t want to be presumptuous in your availability at the time. I will gladly do so in the future, given that the invitation has been issued!
Like I said previously, it pains me that solutions to math problems as simple as these have grown more elusive as I move farther away from my university days. I also realize that I could take steps to re-educate myself, but I am also very lazy…so…