Step 1 :

Pythagorean theorem :

In a right angular triangular hypotenuse is equal to the sum of the squares of the other two sides.

Step 2 :

(a)

The height of the radio tower is 500 ft.

Let the length of the guy wire is z.

Observe the figure :

Evaluation of x :

Evaluation of y :

Evaluation of h :

Step 3  :

From the Pythagorean theorem:

Substitute and in above equation.

The length of the guy wire is 492.6 ft.

Step 3  :

(b)

If the guy wire is connect to the middle of the tower m

Thus, ft.

Let the length of the guy wire is w.

From the Pythagorean theorem:

The length of the second guy wire is 269.3 ft.

Solution  :

(a) The length of the guy wire is 492.6 ft.

(b) The length of the second guy wire is 269.3 ft.