From the attached diagram, we can see that the vector v and vector w form a triangle with an angle of 310-172=138 degrees
Since the vector v+w is the opposite of angle 138 degrees, we can use cosine rule to find the size of vector v+w
[tex] (v+w)^{2} = v^{2} + w^{2} - 2(v)(w) cos(138)[/tex]
[tex] (v+w)^{2} = 136939.6885 [/tex]
[tex]v+w = \sqrt{136939.6885} [/tex]
[tex]v+w = 370.1 (to one dp)
[/tex]
