To determine the [tex]$y$[/tex]-component of the force acting on the block, we follow these steps:
1. Understand the Problem:
- The force applied, [tex]$F$[/tex], is 177 Newtons.
- The angle from the horizontal, [tex]$\theta$[/tex], is [tex]$85.0^{\circ}$[/tex].
2. Convert the Angle to Radians:
- The angle [tex]$\theta$[/tex] should be converted from degrees to radians for the purpose of calculation in trigonometry.
- The conversion formula is:
[tex]\[
\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}
\][/tex]
- Substituting [tex]$\theta = 85.0^{\circ}$[/tex]:
[tex]\[
\theta_{\text{rad}} \approx 85.0 \times \frac{\pi}{180} \approx 1.483529864 \, \text{radians}
\][/tex]
3. Use the Sine Function to Find the [tex]$y$[/tex]-Component:
- The [tex]$y$[/tex]-component of the force, [tex]$F_y$[/tex], is found using the sine function:
[tex]\[
F_y = F \sin(\theta_{\text{rad}})
\][/tex]
- Substituting the given force and the angle in radians:
[tex]\[
F_y = 177 \, \text{N} \times \sin(1.483529864)
\][/tex]
4. Calculate the Sine of the Angle:
- Using a calculator or sine tables, [tex]$\sin(1.483529864)$[/tex] is approximately:
[tex]\[
\sin(1.483529864) \approx 0.999847695
\][/tex]
5. Compute the [tex]$y$[/tex]-Component:
- Multiply the force by the sine of the angle:
[tex]\[
F_y = 177 \, \text{N} \times 0.999847695 \approx 176.326461
\][/tex]
6. Final Answer:
- The [tex]$y$[/tex]-component of the force acting on the block is approximately:
[tex]\[
\overrightarrow{F_y} \approx 176.326 \, \text{N}
\][/tex]
