Question involving vector & magnitude

[I_noscopedJFK]

Homework Statement

"If a vector magnitude 10 is combined with a second vector, the two vectors have a sum with a magnitude of 18 and have a difference with a magnitude of 2√10. Rounded to the nearest hundredth of a degree, what is the measure of the smallest angle between the two vectors?

Homework Equations

cosθ = (u dotproduct v) / (|u||v|)

The Attempt at a Solution

: |u| = 10
: |u+v| = 18
: |u-v| = 2√10


Can you tell me if I'm doing this the right way? If I am, how should I solve this?

 

[vela]

Looks fine so far. Now square the last two equations and write the lefthand sides in terms of the dot product.