Vector a⃗ points in the negative x direction. vector b⃗ points at an angle of 30.0∘ above the positive x axis. vector c⃗ has a magnitude of 19m and points in a direction 37.0∘ below the positive x axis.

given that a⃗ +b⃗ +c⃗ =0, find the magnitudes of a⃗ and b⃗ .

Graph of vectors is in the attachment.
 →           →
| a | = ?,  | b | = ?
We will solve the system of equations:
( 1 )  19 · cos 37° + b · cos 30° - a = 0
( 2 )  19 · sin 37° - b · sin 30° = 0
19 · 0.602 = b · 0.5
11.4345 = 0.5 b
 →
| b | = 22.8869 m
19 · 0.7986 + 22.8869 · 0.866 = a
 →
| a | =  34.995 m

Use a graph site then you will find your answer