Answer:
84.463°
Step-by-step explanation:
Determine the x- and y-components of these two vectors. Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:
x-comps:
5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83
y-comps:
5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562
Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°: ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or
1.474 rad 180°
-------------- * ----------- = 84.463°
1 π
