Question

A telephone pole is installed so that 25 feet of the pole are above ground level. A stabilizing cable is anchored to the ground 44 inches from the base of the pole. The other end of the cable is attached to the pole at a point 20 feet above ground level. To the nearest inch, how many inches long is the stabilizing cable?

Answer 1

$\huge\boxed{244\ \text{inches}}$

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.

$20*12=240$

The length from the base of the pole to the anchor point on the ground is $44$ inches. The distance from the base of the pole to the anchor point on the pole is $240$ 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:

$a^2+b^2=c^2$

In this formula, $a$ and $b$ are the legs and $c$ is the hypotenuse.

Plug in the known values.

$44^2+240^2=c^2$

Swap the sides of the equation.

$c^2=44^2+240^2$

Evaluate the powers.

$c^2=1936+57600$

Simplify using addition.

$c^2=59536$

Take the square root of both sides.

$c=\pm 244$

Separate the solutions.

$c=244\\c=-244$

Length and distance cannot be negative, so remove the negative solution.

$c=\boxed{244}$