Math Help - two forces

1. two forces

two forces of 115 lb and 215 lb acting on an object have a resultant of magnitude 275 lb. find the angle between which the given forces act.

use law of cosines

2. arccos -0.327....
=arccos 0.327..

3. If you can make a sketch, this would help you a lot.

Let's call the force 115 lb being along a vector OA and the 215 lb force along a vector OB. Lastly, OC being the vector along the resultant 275 lb force.

using the cosine rule, we can get the angle OBC.

$275^2 = 215^2 + 115^2 - 2(115)(215)cos OBC$

Now, if you have your sketch, you'll know that OACB is a parallelogram. You are looking for angle AOB, the angle between the two forces. You have OBC and you know that angle OBC = angle OAC and angle AOB = angle ACB. Then, we know that in a quadrilateral, the sum of angles is 360 degrees. You can find angle AOB now.

I hoped it helped!