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:
[tex]\frac{a}{\sin\text{ A}}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
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:
[tex]\sin \text{ B=}\frac{b\sin A}{a}[/tex]
And B will be gotten by the sin inverse of the RHS. Mathematically, thus:
[tex]B=\sin ^{-1}(\frac{b\sin A}{a})[/tex]
Substituting, we get:
[tex]\begin{gathered} B=\sin ^{-1}(\frac{10\times\sin42}{16}) \\ B=\sin ^{-1}0.4182 \\ B=24.72^o \end{gathered}[/tex]
B = 24.72 degrees
