Find Magnitude of Resultant

[mathxyz]

Two forces acting on a body make an angle of 104 degrees with each other. The magnitude of the first force is 390 pounds. If the resultant makes an angle of 47 degrees, what is the magnitude of the resultant, to the nearest tenth of a pound?

I understand that the two forces are not given. I drew a parallelogram and tried finding the two forces but to no avail.

 

[soroban]

Hello, mathxyz!

Is that the exact wording of the problem? .Is there a diagram?
There is some information missing . . .

Two forces acting on a body make an angle of 104 degrees with each other.
The magnitude of the first force is 390 pounds.
If the resultant makes an angle of 47 degrees, . . . with what?
what is the magnitude of the resultant, to the nearest tenth of a pound?

               B              D
                *            * 
                 \         /    
               390\      /     
                   \   /       
                     * - - - - - - *
                     A       ?       C

One force is 390 pounds in the direction AB.
The other force is unknown but is in the direction AC.
Angle BAC = 104°.

The resultant force is the vector AD.
And it makes a 47° angle with what? . with AB? . with AC? . something else?

 

[tkhunny]

Put it on a coordiante axis.

Force = 390 lbs put on the positive x-axis.
"Other" force - Draw the angle at 104° - Label this force A lbs
Resultant Force - Draw the angle at 47° - Label this force B lbs

Equate the horizontal components via the cosine.
Equate the vertical components vie the sine. <== Made convenient by putting one of the forces on the x-axis.

Solve for A and B

Edit: Soroban beat me to it and picked a different order for the vectors.

 

[mathxyz]

hey

To Soroban:

Two forces acting on a body make an angle of 104 degrees with each other. The magnitude of the first force is 390 pounds.
If the resultant makes an angle of 47 degrees, . . . with what?---with the first force what is the magnitude of the resultant, to the nearest tenth of a pound?