We can easily find the value of angle B using the sine rule.
The sine rule is basically a ratio of the sides and sines of angles in a triangle.
It goes thus:

Where a, b, c and A, B, C are sides and opposite angles respectively.
We have a = 16, b = 10, A = 42 degrees, B = unknown.
Making B the subject of the formulae will lead us to cross multiply and get:

And B will be gotten by the sin inverse of the RHS. Mathematically, thus:

Substituting, we get:

B = 24.72 degrees