Answer:
58.9 N [W24.8°N]
Step-by-step explanation:
The vectors are at right angles, so the magnitude of their sum is ...
√(38² +45²) ≈ 58.9 . . . . newtons
The angle Fc makes with Fa can be found using the arctangent:
angle between Fa and Fc = arctan(45/38) ≈ 49.8°
The direction required for the sum of the vectors to be zero is the opposite of [E(49.8° -25°)S], so is [W24.8°N]
The vector that makes the sum zero is 58.9 N [W24.8°N].