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

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

To find the [tex]$ x $[/tex]-component of the total force acting on the chair, you need to consider the contributions from both forces.

### Steps to Calculate the [tex]$ x $[/tex]-component:

1. Identify the Forces and Angles:
- First force [tex]$ F_1 = 122 $[/tex] N at an angle of [tex]$ 43.6^\circ $[/tex].
- Second force [tex]$ F_2 = 97.6 $[/tex] N at an angle of [tex]$ 49.9^\circ $[/tex].

2. Convert Angles to Radians:
- Although calculations were likely done in radians, when understanding manually, they are typically done using degrees on basic calculators. However, computers often use radians.

3. Calculate the [tex]$ x $[/tex]-component for Each Force:
- The [tex]$ x $[/tex]-component of a force can be calculated using the cosine of its angle:
[tex]\[
F_{1x} = F_1 \cdot \cos(43.6^\circ)
\][/tex]
[tex]\[
F_{2x} = F_2 \cdot \cos(49.9^\circ)
\][/tex]

4. Add the [tex]$ x $[/tex]-components:
- Add the [tex]$ x $[/tex]-components of the two forces to get the total [tex]$ x $[/tex]-component:
[tex]\[
F_x = F_{1x} + F_{2x}
\][/tex]

### Results:

- [tex]$ F_{1x} $[/tex]: This component is approximately 88.35 N.
- [tex]$ F_{2x} $[/tex]: This component is approximately 62.87 N.
- Total [tex]$ x $[/tex]-component ([tex]$ F_x $[/tex]): By summing these components, the total [tex]$ x $[/tex]-component is approximately 151.22 N.

So, the [tex]$ x $[/tex]-component of the total force acting on the chair is around 151.22 N.