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°. 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 trigonometry.
First, let's label the given information:
- The height of the servers' stand is 5 feet.
- The height of the kitchen is 1 foot.
- The angle of elevation from the kitchen to the servers' stand is 25°.
We can use the tangent function to find the length of the cable:
tan(angle) = opposite / adjacent
In this case, the opposite side is the height difference between the servers' stand and the kitchen, and the adjacent side is the length of the cable.
Let's calculate the length of the cable:
tan(25°) = (5 - 1) / adjacent
Simplifying the equation:
tan(25°) = 4 / adjacent
Now, we can solve for the adjacent side, which represents the length of the cable:
adjacent = 4 / tan(25°)
Using a calculator, we find that the value of tan(25°) is approximately 0.4663.
Substituting this value into the equation:
adjacent = 4 / 0.4663 ≈ 8.58 feet
Therefore, the length of the cable is approximately 8.58 feet.
To calculate the length of the cable, we can use trigonometry. In this case, we will be using the tangent function since we have the angle and the opposite side length.
First, let's identify the right triangle formed by the cable, with the 5-foot side as the opposite side and the length of the cable as the hypotenuse. The adjacent side will be the difference in height between the two ends of the cable, which is 5 ft - 1 ft = 4 ft.
Now, we can apply the tangent function:
tan(angle) = opposite/adjacent
tan(25°) = 5 ft / 4 ft
To solve for the length of the cable, we can rearrange the equation:
length of cable = opposite / tan(angle)
length of cable = 5 ft / tan(25°)
Using a calculator, we can find the length of the cable to the nearest hundredth of a foot:
length of cable ≈ 9.51 ft
Therefore, the length of the cable is approximately 9.51 feet.