[tex]\begin{gathered} x-\text{component}=6.26 \\ \text{y-component=8.30} \end{gathered}[/tex]
Explanation
Step 1
when you have a vector, you have a rigth triangle formed by, the vector, the x-axis and the vertical line
where
hypotenuse=5
angle=37 degrees
x-component=adjacent side
y-component= opposite side
Step 2
[tex]\begin{gathered} \cos \text{ }\alpha=\frac{hyp}{\text{adjacent side}} \\ \text{adjacent side=}\frac{hypotenuse}{\cos\text{ }\alpha} \\ \text{adjacents side=}\frac{5}{\cos\text{ 37}}=6.26 \\ x-\text{component}=6.26 \end{gathered}[/tex]
Step 3
[tex]\begin{gathered} \sin \text{ }\alpha=\frac{hyp}{\text{opposite side}} \\ \\ \text{opposite side=}\frac{hyp}{\sin \text{ }\alpha} \\ \text{opposite side=}\frac{5}{\sin \text{ 37}} \\ \text{opposite side=y-component=8.30} \\ \text{y-component=8.30} \end{gathered}[/tex]
I hope this helps you
