a restaurant uses a cable for the servers to slide orders down to the kitchen. the end where the servers place the order is 5 feet high. the end where the kitchen receives the order is 1 foot high. the angle of elevation from the kitchen to the servers stand is 25 degrees. calculate the length of the cable to the nearest hundredth of a foot.

the difference in heights is 4

x = cable length

sin 25° = 4/x
x = 4/sin25° = 9.46

To calculate the length of the cable, we can use the concept of trigonometry. Specifically, we can use the tangent of the angle of elevation.

Let's denote the length of the cable as "x."

Using the tangent function, we have:

tan(25 degrees) = (height difference)/(length of the cable)

We can rearrange this equation to solve for the length of the cable:

length of the cable = (height difference) / tan(25 degrees)

The height difference is the vertical distance between the two ends of the cable, which is 5 - 1 = 4 feet.

Now, let's substitute the values into the equation:

length of the cable = 4 / tan(25 degrees)

Using a scientific calculator, we can evaluate the tangent of 25 degrees, which is approximately 0.4663.

Therefore, the length of the cable is:

length of the cable = 4 / 0.4663 ≈ 8.59 feet.

Rounding to the nearest hundredth of a foot, the length of the cable is approximately 8.59 feet.