# Resultant of 100N 30 degrees E of N; 200N 80 degrees S of E; 150N 45 degrees S of W; 175N 25 degrees W of N and 50N towards North.

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Forces are vectors: their magnitude as well as a direction has to be considered when working with them.

You want to know the resultant force of 5 forces.

- 100 N acting in a direction 30 degrees east of north
- 200 N acting in a direction 80 degrees south of east
- 150 N acting in a direction 45 degrees south of west
- 175 N acting in a direction 25 degrees west of north
- 50 N acting in the north direction

First let us divide the forces into their components in the north, south, east and west direction.

1. 100*cos 30 towards north and 100*sin 30 towards east

2. 200*cos 80 towards east and 200*sin 80 towards south

3. 150*cos 45 towards west and 150*sin 45 towards south

4. 175*cos 25 towards north and 175* sin 25 towards west

5. 50 N towards the north

Find the net force towards the west , that will include the negative of all forces towards the east.

150*cos 45 + 175* sin 25 - 100*sin 30 - 200*cos 80 = 95.29

Find the net force towards the north, this will include the negative of all forces towards the south.

100*cos 30 + 175*cos 25 + 50 - 200*sin 80 - 150*sin 45 = -7.82

**The resultant force is 95.61 N in the direction 1.43 degrees south of west.**