Question 273868
Let A be the distance from the ground to the coupling C (perpendicular to the ground and parallel to both poles)
Let D be the distance from the tallest poll to the point on the ground from C.

(Angle-Angle (AA) Similarity) two pair of similar triangles are formed.
Using proportions on the smaller pair of triangles to find the distance on the ground from under C to the largest pole.
{{{(30/40) = (a/d)}}} 
30d = 40a
for the larger pair of triangles
{{{(50/40) = (a/40-d)}}}  
50(40-d) = 40a

Notice 40a, substituting on both equations
30d)=50(40-d)
30a = 2000-50d
80d = 2000
d = 25 feet. If you subtract from 40 you get the other base which is 15ft.

Substitute to find the height of the coupling
30d = 40a
30(25)=40a
a=750/40
a=18.75 feet height.

How far down the wire from the smaller pole is the coupling?
Notice that the smaller pole formed a dilation by a factor 10 from a 3,4,5 triangle. Therefore, the wire from the smaller pole to the base of the larger is 50ft. Then using the Triangle Proportionality Theorem, formulate the following proportion. 
Let y be the distance of the segment from the pole to C (Coupling) use the proportion.
{{{y/15=50/40}}}
{{{y=(750/40)}}}
y=18.75 feet
For the distance from C to the Taller pole, using Pythagoras 
{{{c^2=50^2+40^2}}} the hypotenuse is about 64 feet round to the unit.

To find the distance from C to the taller pole, again use the Triangle Proportionality Theorem..
Let p be the distance from C to the Taller pole.
{{{p/25=64/40}}}
The distance is 40 feet.