Answer:
[tex]x = 12.027N[/tex] and [tex]y = 8.964N[/tex]
Explanation:
The first sentence of this question is not explanatory enough. However, I'll assume the force to be 15N
[tex]Force = 15N[/tex]
[tex]\theta = 36.7[/tex] to the horizontal
Required
Solve for the x and y components
Since the given angle is to the horizontal, the x and y coordinates are calculated using the following illustrations.
[tex]Sin\theta = \frac{y}{Force}[/tex] ---- y component
[tex]Cos\theta = \frac{x}{Force}[/tex] ---- x component
Calculating the y component.
Substitute 15 for Force and 36.7 for [tex]\theta[/tex]
[tex]Sin\theta = \frac{y}{Force}[/tex] becomes
[tex]Sin(36.7) = \frac{y}{15}[/tex]
Make y the subject
[tex]y = 15 * Sin(36.7)[/tex]
[tex]y = 15 * 0.5976[/tex]
[tex]y = 8.964N[/tex]
Calculating the x component.
Substitute 15 for Force and 36.7 for [tex]\theta[/tex]
[tex]Cos\theta = \frac{x}{Force}[/tex] becomes
[tex]Cos(36.7) = \frac{x}{15}[/tex]
Make y the subject
[tex]x = 15 * Cos(36.7)[/tex]
[tex]x = 15 * 0.8018[/tex]
[tex]x = 12.027N[/tex]
Hence, the x and y components of the force are: 8.964N and 12.027N respectively.
