Particle statistics- Three forces on force table

[shogunultra]

Particle statics- Three forces on force table

I have the following problem:

Three forces of magnitude 10, 25, 30 dynes are in equilibrium on a force table.

a) find the angles between the forces algebraicly.

b) find the angles graphically

Here is how I attempted to solve a):

I considered one force to be my "force of reference", making it parallel to the x-axis and its vector pointing towards positive x.

Then I tried to find the angles that the other forces make with the x-axis by means of a two equation system, one for the X and one for the Y components of the forces, from which I know that their sum must equate 0.

Im stumped here, equation contains the angles in their sin form and the other contains them as cos, so not knowing any angle doesn't really give me two unknowns, but four.

Thankyou.

 

[andrevdh]

The resultant of the three forces need to be zero. Which means that the three vectors will form the sides of a triangle.

 

[shogunultra]

That would be the graphic way, but a) requests you to solve it algebraeicly.

 

[WyldFyr]

I would think carefully about what andrevdh said, and dust off the old trig. textbook.
Think of the problem as a SSS triangle, and then think Law of Cosines.
Good Luck!