the difference in heights is 4
x = cable length
sin 25° = 4/x
x = 4/sin25° = 9.46
x = cable length
sin 25° = 4/x
x = 4/sin25° = 9.46
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.