Vis a vector 24.8 units in magnitude and points at an angle of 23.4 ∘ above the negative x axis. sketch this vector. calculate vx and vy. use vx and vy to obtain (again) the magnitude of v use vx and vy to obtain (again) the direction of v .

According to the figure

Vx= - Vcos 23.4° = - 24.8*0.9= -22.76
Vy= Vsin23.4°= 9.84
  refind magnitude of V
V= sqrt(V²x  + V²y)=sqrt( -22.76² + 9.84²)=24.79

its direction
let's consider Vy= Vsin x°, x° is assumed as unknown angle

so sinx=Vy/V= 0.39, so x=arcsin(0.39)=23.38, x=23.38° near 23.4°