Final answer:
The length of the guy wire from the top of the cell tower to the metal stake in the ground is 36 feet when adding the hypotenuse of the right triangle formed by the 12-foot pole and its 5-foot base to the 23 feet measured from the pole to the tower.
Step-by-step explanation:
To find the length of the guy wire from the top of the cell tower to the metal stake in the ground, we need to use the Pythagorean theorem in a two-step process. The overall scenario forms two right triangles: one smaller triangle between the pole and the stake and one larger triangle between the tower and the stake.
First, let's find the length of the guy wire supporting the 12-foot tall pole. Given that Feng measures 5 feet from the stake to the pole, we can find the length of the hypotenuse (guy wire) using the Pythagorean theorem (a² + b² = c²), where 'a' is one side, 'b' is the other side, and 'c' is the hypotenuse.
Let's calculate:
- a = 12 feet (height of the pole)
- b = 5 feet (distance from the stake to the pole)
- c = √(a² + b²)
c = √(12² + 5²) = √(144 + 25) = √169 = 13 feet
Therefore, the length of the guy wire supporting the 12-foot tall pole is 13 feet. However, this is not the final answer as we still need to consider the part of the guy wire from the pole to the tower. To find the total length of the guy wire, we need to add the 23 feet measured by Feng from the pole to the tower. Hence, the total length of the guy wire is:
13 feet (length from stake to pole) + 23 feet (length from pole to tower) = 36 feet.
The length of the guy wire to the nearest foot is therefore 36 feet.