3 equations 3 unknowns

From (1) 0.259 v^2 = w^2 sin^2 x
From (2) (5.318 - 0.8607v)^2 = w^2 cos^2 x
Adding the two together we get
0.259 v^2 + (5.318 - 0.8607v)^2 = w^2.
Sub. into eqt. (3)
28.2857 = v^2 + 0.259v^2 + (5.318 - 0.8607v)^2
2v^2 - 9.1544 v = 0 ( to 2 dp)
so v = 0 or 4.5772.
For v = 0, w = 5.318, x = 0.
For v = 4.5772, w = 2.7083, x = 59.35 degree.

Let a=5.318, b=30.6, c=2.97/0.105 Squaring equation 2, a2=v2cos2b+w2cos2x+2vwcosbcosxa2=v2(1-sin2b)+w2(1-sin2x)+2vwcosbcosxa2=v2+w2+2vwcosbcosx-(v2sin2b+w2sin2x)a2=c+2vwcosbcosx-2v2sin2b equation 1+3a2=c+(2vcosb)(a-vcosb)-2v2sin2b equation 2a2=c+2avcosb-(2v2cos2b+2v2sin2b)a2=c+2avcosb-2v2(2)v2-(2acosb)v+(a2-c)=0 by quadratic formula,v=4.577927449 or -5.013497625x10-4substituting into equation 3,w=2.707082295 or 5.318431539substituting into equation 1,x=59.41061115 or -2.749368743x10-3
for (v,w,x)=(4.577927449, -2.707082295, -59.41061115) and (v,w,x)= -(5.013497625x10-4, -5.318431539, 2.749368743x10-3), these are not solution as they cannot be a solution for equation 2