Answer:
39.05 pounds at [tex]60.19^{\circ}[/tex]
Explanation:
To find the resultant force, we need to decompose each vector along the x- and y- directions. Let's do it:
Vector 1:
[tex]A_x = 25 \cdot cos 10^{\circ}=24.62[/tex]
[tex]A_y = 25 \cdot sin 10^{\circ}=4.34[/tex]
Vector 2:
[tex]B_x = 30 \cdot cos 100^{\circ}=-5.21[/tex]
[tex]B_y = 30 \cdot sin 100^{\circ}=29.54[/tex]
Resultant components:
[tex]R_x = A_x + B_x =24.62+(-5.21)=19.41[/tex]
[tex]R_y = A_y + B_y = 4.34+29.54 =33.88[/tex]
So the magnitude of the resultant is
[tex]R=\sqrt{R_x^2+R_y^2}=\sqrt{(19.41)^2+(33.88)^2}=39.05[/tex]
And the direction is
[tex]\theta=tan^{-1}(\frac{R_y}{R_x})=tan^{-1}(\frac{33.88}{19.41})=60.19^{\circ}[/tex]
