Step 1:
Draw the vector diagram
Step 2:
Write the angles to the horizontal axis.
30 degrees to the horizontal axis = 30
150 degrees to the horizontal axis = 180 - 150 = 30
Step 3:
Find the vertical component and the horizontal component of the magnitude.
[tex]\begin{gathered} \text{Horizontal component = Fcos}\theta \\ \text{Vertical component = Fsin}\theta \end{gathered}[/tex]
Step 3:
[tex]\begin{gathered} \text{Sum of the vertical component V = 25 + 30 = 55} \\ \text{Sum of the horizontal component H = 43.3 - 51.96 = -8.66} \end{gathered}[/tex]
Step 4:
Find the magnitude
[tex]\begin{gathered} \text{Magnitude = }\sqrt[]{V^2+H^2} \\ =\text{ }\sqrt[]{55^2+(-8.66)^2} \\ =\text{ }\sqrt[]{3025+74.9956} \\ =\text{ 56.678} \end{gathered}[/tex]
Magnitude = 56.678
Step 5:
Find the direction
[tex]\begin{gathered} \text{Tan}\theta=\text{ }\frac{V}{H} \\ \theta=tan^{-1}(\frac{55}{8.66}) \\ \theta\text{ = 81} \end{gathered}[/tex]
Direction = 81
