Four wires support a 40-meter radio tower. Two wires are attached to the top and two are attached to the center of the tower. The wires are anchored to the ground 30-meters from the base of the tower.
What is the total length of wire needed?
To find the total length of wire needed for the tower, let's break down the problem:
1. Start with the two wires attached to the top of the tower. Since the tower height is 40 meters, these wires will each have a length of 40 meters.
2. Now let's consider the two wires attached to the center of the tower. These wires are anchored to the ground 30 meters from the base of the tower. Since they are attached to the center, they form a right triangle with the tower. The height of this right triangle is half of the tower's height, which is 40/2 = 20 meters.
3. The length of the hypotenuse of this right triangle represents the length of each of the two wires attached to the center of the tower. We can find the length of the hypotenuse using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the other two sides. In this case, a = 20 meters and b = 30 meters. Plugging these values into the formula, we get c^2 = 20^2 + 30^2 = 400 + 900 = 1300. Therefore, c = √1300 ≈ 36.06 meters.
4. Since there are two wires attached to the center of the tower, the total length of wire needed for these wires is 2 * 36.06 = 72.12 meters.
5. Finally, to find the total length of wire needed for the tower, we add up the lengths of all the wires: 40 + 40 + 72.12 = 152.12 meters.
Therefore, the total length of wire needed for the tower is approximately 152.12 meters.
You have two wires of length 50 and two wires of length 10√13
add them up