There are two 100-foot poles. A 150-foot rope connects them at the top. The bottom of the rope hangs to 25 feet from the ground. How far apart are the poles?
Huh? If the poles are 100 feet tall, then it takes 75 feet of rope to reach to within 25 feet of the ground. So, if the rope is 150 feet long, it just hangs 75 feet straight down and back up. The two poles are 0 feet apart.
To find the distance between the two poles, we need to use the concept of similar triangles. Let's break down the problem.
We have two poles that are 100 feet tall, and they are connected at the top by a rope.
The bottom of the rope hangs 25 feet from the ground.
To find the distance between the poles, we can create a right triangle using one of the poles, the ground, and a segment of the rope.
Let's call the distance between the poles "x".
Using the concept of similar triangles, we can set up a proportion to find x.
The height of the first pole is 100 feet, and the length of the rope from the top to the bottom is 100 feet + 25 feet = 125 feet.
In the right triangle we created, the long leg (125 feet) is proportional to the hypotenuse (the distance between poles, x).
So we can set up the following proportion:
100/125 = x/150
Cross-multiplying gives us:
100 * 150 = 125 * x
Simplifying:
15,000 = 125 * x
To solve for x, we divide both sides by 125:
15,000 / 125 = x
x = 120
Therefore, the distance between the poles is 120 feet.