A chair is pulled by two horizontal forces. The first force is 122 N at an angle of [tex]$43.6^{\circ}$[/tex], and the second is 97.6 N at an angle of [tex]$49.9^{\circ}$[/tex].

What is the [tex]$x$[/tex]-component of the total force acting on the chair?

[tex]\overrightarrow{F_x} = [?] \, \text{N}[/tex]

To find the x-component of the total force acting on the chair, we need to calculate the x-components of each individual force and then add them together. Here’s how we can do it:

1. Understand the Forces:
- We have two forces acting on the chair.
- The first force is 122 N at an angle of 43.6° from the horizontal.
- The second force is 97.6 N at an angle of 49.9° from the horizontal.

2. Resolve Each Force into Its Components:
- The x-component of a force can be found using the formula:
[tex]\[
F_x = F \times \cos(\theta)
\][/tex]
where [tex]$ F $[/tex] is the magnitude of the force and [tex]$ \theta $[/tex] is the angle the force makes with the horizontal axis.

3. Calculate the x-component of the First Force:
- For the first force, [tex]$ F_1 = 122 $[/tex] N and the angle [tex]$ \theta_1 = 43.6^\circ $[/tex].
- So, the x-component is:
[tex]\[
F_{1x} = 122 \times \cos(43.6^\circ) \approx 88.35 \, \text{N}
\][/tex]

4. Calculate the x-component of the Second Force:
- For the second force, [tex]$ F_2 = 97.6 $[/tex] N and the angle [tex]$ \theta_2 = 49.9^\circ $[/tex].
- So, the x-component is:
[tex]\[
F_{2x} = 97.6 \times \cos(49.9^\circ) \approx 62.87 \, \text{N}
\][/tex]

5. Find the Total X-component of the Forces:
- Add the x-components of both forces to get the total x-component:
[tex]\[
\overrightarrow{F_x} = F_{1x} + F_{2x} = 88.35 \, \text{N} + 62.87 \, \text{N} = 151.22 \, \text{N}
\][/tex]

Thus, the x-component of the total force acting on the chair is approximately [tex]$ 151.22 \, \text{N} $[/tex].