Question

The cable is attached to the boom at point A and to point B as shown in Figure 1. The values of x, y, and z are given as x = 60 ft, y = 40 ft, and z = 40 ft. What is the length of the cable?

Answer 1

To find the length of the cable connecting points A and B with dimensions x = 60 ft, y = 40 ft, and z = 40 ft, use the Pythagorean theorem in three dimensions, resulting in the cable's length being the square root of 6800 feet.

Step-by-step explanation:

The question requires calculating the length of the cable connecting points A and B. Given the dimensions x = 60 ft, y = 40 ft, and z = 40 ft, the cable's length can be found by employing the Pythagorean theorem for a three-dimensional space, which states that the length of the cable (L) is the square root of the sum of the squares of the sides, or L = sqrt(x^2 + y^2 + z^2). Plugging in the given values, we get L = sqrt(60^2 + 40^2 + 40^2) feet.

By calculating numerically, we get L = sqrt(3600 + 1600 + 1600) feet, which simplifies to L = sqrt(6800) feet. Therefore, the cable length is the square root of 6800 feet, which needs to be calculated to get the final result.