[tex]\huge\boxed{244\ \text{inches}}[/tex]
This problem can be solved using the Pythagorean Theorem.
Note: the height of the telephone pole is unnecessary information.
Convert the measurement in feet to inches.
[tex]20*12=240[/tex]
The length from the base of the pole to the anchor point on the ground is [tex]44[/tex] inches. The distance from the base of the pole to the anchor point on the pole is [tex]240[/tex] inches.
These are the two legs of a right triangle. The length of the stabilizing cable is the hypotenuse of the right triangle.
The Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
In this formula, [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
Plug in the known values.
[tex]44^2+240^2=c^2[/tex]
Swap the sides of the equation.
[tex]c^2=44^2+240^2[/tex]
Evaluate the powers.
[tex]c^2=1936+57600[/tex]
Simplify using addition.
[tex]c^2=59536[/tex]
Take the square root of both sides.
[tex]c=\pm 244[/tex]
Separate the solutions.
[tex]c=244\\c=-244[/tex]
Length and distance cannot be negative, so remove the negative solution.
[tex]c=\boxed{244}[/tex]
