Answer:
[tex]38.6^{\circ}[/tex]
Explanation:
In order to find the resultant of the two vectors, we need to find the components of each vector along the x- and y- axis.
For the horizontal vector, we have:
x-component: [tex]A_x = 15[/tex]
y-component: [tex]A_y = 0[/tex]
For the vectors of 18 units:
x-component: [tex]B_x = 18 cos 70^{\circ}=6.16[/tex]
y-component: [tex]B_y = 18 sin 70^{\circ}=16.91[/tex]
So the components of the resultant vector are
[tex]R_x=A_x + B_x = 15 +6.16 = 21.16[/tex]
[tex]R_y=A_y + B_y = 0 +16.91 = 16.91[/tex]
And so the direction is given by
[tex]\theta = tan^{-1} (\frac{R_y}{R_x})=tan^{-1} (\frac{16.91}{21.16})=38.6^{\circ}[/tex]
