This problem can be solved using the Pythagorean Theorem.
<em>Note: the height of the telephone pole is unnecessary information.</em>
Convert the measurement in feet to inches.
The length from the base of the pole to the anchor point on the ground is inches. The distance from the base of the pole to the anchor point on the pole is
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:
In this formula, and
are the legs and
is the hypotenuse.
Plug in the known values.
Swap the sides of the equation.
Evaluate the powers.
Simplify using addition.
Take the square root of both sides.
Separate the solutions.
Length and distance cannot be negative, so remove the negative solution.