At what angle must one cut the board?

Question

Given a 2" wide board and a 1 1/2" wide board, we would like to cut the narrower board at an angle $\theta$ so the cut is 2" long so the boards will fit together as shown in the diagram below. At what angle $\theta$ should we cut the board?

Here's what I have so far. Is this correct?

\begin{gather} \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \\ 1.5 / 2 = 0.75 \\ \cos^{-1}(0.75) = 41.40962211 \text{degrees} \end{gather}

Answer 1

As you can see in the photo above, 1.5" is actually the opposite side instead of the adjacent side. Therefore, the answer should be $\arcsin(\frac{1.5}{2}) ≈ 48.59°$.