Precalculus, Chapter 6, 6.4, Section 6.4, Problem 32

You need to use the formula of dot product to find the angle between two vectors, u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u*v = |u|*|v|*cos(theta)
The angle between the vectors u and v is theta.
cos theta = (u*v)/(|u|*|v|)
First, you need to evaluate the product of the vectors u and v, such that:
u*v = u_x*v_x + u_y*v_y
u*v = 3*4 + 2*(0)
u*v = 12
You need to evaluate the magnitudes |u| and |v|, such that:
|u|= sqrt(u_x^2 + u_y^2) => |u|= sqrt(3^2 + 2^2) =>|u|= sqrt13
|v|= sqrt(v_x^2 + v_y^2) => |v|= sqrt(4^2 + 0^2) => |v|= 4
cos theta = (12)/(4sqrt13) => cos theta = (3)/(sqrt13)
Hence, the cosine of the angle between the vectors u and v is cos theta = (3)/(sqrt13) , so, theta ~~ 34^o.