A force having magnitude of 360 newtons is acting in the direction of North.
If it is resolved into two perpendicular components, find the value of the component acting in the direction of East, if it exists.
After resolving the force into two perpendicular components, if a component existed in the easterly direction, the force would no longer be acting purely to the north.
Therefore, however we resolve the force into perpendicular components, there will never be a component in the easterly direction.
Ultimately, this is as a result of the fact that east is perpendicular to the direction of the force.