# A force of 90 lb acts on an object at an angle of 55 degrees. A second force of 100 lbs acts on the object at an angle of -60 degrees. Find the direction and magnitude of the resultant force.

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Expert Answers

tiburtius | Certified Educator

First force is not measured in pounds but in newtons so I will pretend the forces are 90 N and 100 N.

Now we can calculate the magnitude of resultant force by using law of cosine (see the image below).

`R^2=90^2+100^2-2*90*100*cos65^o=10493.2`

`R=102.4363` **<-- Magnitude**

Now we can calculate the direction. In order to do that we will first calculate the angle between vector `veca` and resultant vector `vecR` by using law of sine.

`sin alpha/100=sin65^o/102.4363`

`alpha=62^o13'16''` ` `

Now we subtract that from 55° (direction of vector `vecb` ) to get direction of resultant force.

`55^o-62^o13'16''=-7^o13'16''` **<-- Direction**