Question

A 15.0 m telephone pole is beginning to lean as the soil erodes.a cable is attached 5.0 m from the top of the pole to prevent the polefrom leaning any farther. the cable is secured 10,2 m from the base ofthe pole. determine the length of the cable that is needed if the pole isalready leaning 7° from the vertical.

Answer 1

To determine the length of the cable needed to prevent the pole from leaning any farther, use trigonometry. By using the tangent function with the angle of lean, the length of the cable can be calculated to be approximately 39.5 meters.

Step-by-step explanation:

To determine the length of the cable needed to prevent the pole from leaning any farther, we can use trigonometry. The cable forms a right triangle with the pole and the ground. We know the length of the pole (15.0 m) and the height from the base to where the cable is secured (10.2 m). We also know the angle of lean (7°) from the vertical. Using the tangent function, we can calculate the length of the cable as follows:

Tan(7°) = (15.0 m - 10.2 m) / x

Solving for x, the length of the cable:

x = (15.0 m - 10.2 m) / Tan(7°)

Plugging in the numbers:

x = (4.8 m) / Tan(7°)

x ≈ 39.5 m

Therefore, the length of the cable needed is approximately 39.5 meters.