Question

Math Equation Response Question A 103-foot wire is used to support a utility tower. It runs from the tower to the ground and forms a 24° angle with the ground. Use the values in the table to calculate the following (round your answer to the nearest tenth). The distance from the base of the utility tower to the location where the wire is attached to the ground is how many feet? Round your answer to the nearest tenth.

Answer 1

To find the distance from the base of the utility tower to the location where the wire is attached to the ground, use the sine function and the given angle and wire length. The distance is approximately 39.1 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometry. We have a right triangle formed by the utility tower, the wire, and the ground. The angle between the wire and the ground is given as 24 degrees. The length of the wire is given as 103 feet. We can use the sine function to find the distance from the base of the utility tower to the location where the wire is attached to the ground.

Let x be the distance from the base of the utility tower to the attachment point on the ground. We have the equation sin(24) = x/103. To find x, we can rearrange the equation as x = 103 * sin(24). Using a calculator, we find that x is approximately 39.1 feet.