## To understand the problem, imagine a horizontal wire that is stretched between two vertical poles. When a weight of 12.0 Newtons (N) is suspended at the center of the wire, the wire sags until the angle between its halves is 110 degrees. You are asked to find the forces exerted by each half of the wire in supporting the weight.

To solve this problem, follow these steps:

1) Assume symmetry: Since the wire is stretched horizontally and the weight is at the center, we can assume that each half of the wire is symmetrical and experiencing equal forces.

2) Draw a triangle: Draw a triangle representing one half of the wire sag and the horizontal line across the top. Label the angles of the triangle as follows: 55 degrees (half of 110 degrees), 90 degrees (at the top), and 35 degrees (half of 70 degrees).

3) Identify the known and unknown quantities:

- Known: The weight suspended at the center is 12.0 N.

- Unknown: The forces exerted by each half of the wire.

4) Apply geometry and trigonometry: From the triangle, we can see that the weight of 12.0 N is exerting a downward force on each half of the wire. Let's call the tension in each half of the wire "T". Since the weight is divided equally, each half has a downward force of 12.0 N / 2 = 6.0 N.

5) Use trigonometry to relate the tension to the sag angle: The tension force can be related to the angle of sag using trigonometry. In this case, the equation is T/6 = sin(35 degrees).

6) Solve for tension: Rearrange the equation to solve for T: T = 6 * sin(35 degrees). Use a calculator to compute sin(35 degrees) and multiply it by 6. The value you obtain is the force exerted by each half of the wire in supporting the weight.

By following these steps, you should be able to find the forces exerted by each half of the wire when a weight of 12.0 N is suspended at its center.