Physics

The key insight is that the $y$-components of vectors add independently—so if the resultant has zero $y$-component, the $y$-components of $\mathbf{A}$ and $\mathbf{B}$ must cancel each other out. Start by finding $\mathbf{B}$'s $y$-component in terms of $b$ using the angle, then set up an equation that forces the total $y$-component to zero.

The key insight is that the $y$-components of vectors add independently—so if the resultant has zero $y$-component, the $y$-components of $\mathbf{A}$ and $\mathbf{B}$ must cancel each other out. Start by finding $\mathbf{B}$'s $y$-component in terms of $b$ using the angle, then set up an equation that forces the total $y$-component to zero.