Posted by **Iamxe** on Sunday, May 11, 2008 at 12:28pm.

A force of 369 lbs makes an angle of 18 degrees 20 minutes with a force 427 lbs. Find the angle made by the equilibrant with the 369 lbs force.

I know I can find this using the law of cosines, but I think my teacher wants me to use some vector thing, but I do not know how to relate the two vectors to the equilibrant. Is it like u-v?

- precalculus -
**bobpursley**, Sunday, May 11, 2008 at 2:03pm
Hmmm. use the 427 Lbs at 0 degrees, then the cos18'20" * 369 is the force in the direction of zero degrees, and 369*sin18'20"is the force 90 degrees to that. Now add these two to see the resulatant, and then add180 degrees to get the equilibrant.

- precalculus -
**Damon**, Sunday, May 11, 2008 at 2:15pm
Well, either way it is a "vector thing.

The "equilibrant" is equal and opposite to the "resultant" or sum of the two vectors. In other words it is the vector needed to cancel them.

I will find the resultant, then we can do minus signs.

I am going to say we have 369 pounds along the x axis and 427 pounds at 18 1/3 degrees above the x axis.

In vector notation that is

Rx = 369 + 427 cos 18.33

Ry = 427 sin 18.33

or

Rx = 369 + 405 = 774

Ry = 134

Our equilibrant has components then

Ex = -774

Ey = -134

That is in the third quadrant at

tan A = 134/774 where A is below the -x axis

A = 9.82 degrees below -x axis

or

189.8 degrees counterclockwise from x axis where our original 369 lb force was

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