A guy wire (a tensioned cable designed to add stability to a free-standing structure) is attached to a telephone pole whose height is 25 ft. If the wire is attached to the ground at a point 15 ft away from the base of the pole, what is the slope of the wire?

To find the slope of the guy wire, we can use the concept of similar triangles. The guy wire, telephone pole, and the segment from the base of the pole to the point where the wire is attached on the ground form a right triangle.

Let's consider the right triangle formed by the guy wire, the telephone pole, and the segment from the base of the pole to the point where the wire is attached on the ground.

The height of the telephone pole is given as 25 ft, and the distance from the base of the pole to the point where the wire is attached on the ground is given as 15 ft.

The slope of the guy wire can be determined by finding the ratio of the height to the distance from the base. This ratio will be the same as the ratio of the corresponding sides of the similar triangles.

Therefore, the slope of the guy wire can be calculated as:
Slope = height / distance from the base = 25 ft / 15 ft

Simplifying the expression, we find:
Slope = 5/3

So, the slope of the guy wire is 5/3.

To find the slope of the guy wire, we can use trigonometry. The slope of the guy wire can be represented as the ratio of the vertical distance (height) to the horizontal distance. In this case, the height of the telephone pole is given as 25 ft, and the distance between the wire attachment point on the ground and the base of the pole is 15 ft.

To determine the slope, we need to find the ratio of the change in height to the change in horizontal distance. In this case, the change in height is the height of the pole, which is 25 ft, and the change in horizontal distance is the distance from the base of the pole to the wire attachment point on the ground, which is 15 ft.

Using the formula for slope (rise over run), we can calculate the slope of the guy wire:

Slope = Change in height / Change in horizontal distance

Slope = 25 ft / 15 ft

Slope = 5/3 or approximately 1.67

So, the slope of the guy wire is 5/3 or approximately 1.67.

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