Question 939326
Hint: Draw the two vectors where their tails start at the same point. The first vector u is in black while the other vector v is in blue. The angle between the two vectors is shown in purple the angle {{{alpha}}}. Use the parallelogram rule to help you construct the red resultant vector {{{u+v}}}


<img src = "http://i150.photobucket.com/albums/s91/jim_thompson5910/986h6c5wb8pu90txpc92_zps10eaa74f.png">


You can use the formula {{{cos(alpha) = (u*v)/(abs(u)*abs(v))}}} to find the angle {{{alpha}}}. Note: u and v are vectors, so when I say {{{u*v}}} I mean "dot product of u and v".


We're dealing with a parallelogram. So the adjacent angles are supplementary meaning that {{{alpha + theta = 180}}}. Use the value of alpha to find theta.


Once you know theta, you can then use the law of cosines {{{c^2 = a^2+b^2 -2ab*cos(C)}}} to find the length of the red resultant vector which will be your answer.