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

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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 .

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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 .