Question

A power line is connecting the top of a building to the ground 260 meters away from the base of the building. At what angle is the wire connected at the building if the wire is 340 meters long.

Answer 1

Using the cosine function, the angle of connection for the power line at the building is approximately 53.13°, calculated by taking the inverse cosine of the ratio of the adjacent side (260 meters) to the hypotenuse (340 meters).

Step-by-step explanation:

Finding the Angle of Connection for a Power Line

To find the angle at which the power line is connected to the building, we can apply trigonometric functions, specifically the cosine function, which is part of the cosine rule or the law of cosines. Since we have a right-angled triangle, we can use the adjacent side (the distance from the building's base to where the wire meets the ground, 260 meters) and the hypotenuse (the length of the wire, 340 meters).

The cosine of the angle θ can be found by dividing the adjacent side by the hypotenuse:

cos(θ) = adjacent/hypotenuse

cos(θ) = 260 meters / 340 meters

We then take the inverse cosine (arccos) to find the angle θ:

θ = arccos(260/340)

Using a calculator, we find that θ ≈ 53.13°, which is the angle at which the wire is connected to the building.

The angle of connection for the wire at the building is approximately 53.13°.