In triangle vuw the measure of angle v equals (15y+9), the measure of angle u equals (22y+8),and the measure of angle w equals (14y+10) . which side length is the smallest?

We know that the sum of the interior angles of every triangle is 180°:
( 15 y + 9° ) + ( 22 y + 8° ) + ( 14 y + 10° ) = 180°
15 y + 22 y + 14 y = 180° - 9 ° - 8° - 10°
51 y = 153°
y = 153° : 51
y = 3°
∠ V = 15 · 3° + 9° = 54°
∠ U = 22 · 3° + 8° = 74°
∠ W = 14 · 3° + 10° = 52°
Let`s assume that opposite the angles V, U and W are sides v , u and w. Opposite the smallest angle is the smallest side of a triangle.
Side length w is the smallest.

The answer is the magnetosphere.