To solve we use the law of sines, of which we have the following equation:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex]
We have the triangle shown below.
As you can see, we start by assuming a right angle at the face angle to the 12' segment.
In this case, the values of the equation for the triangle are as follows
[tex]\begin{gathered} a=4 \\ b=12 \\ \sin (A)=\sin (A) \\ \sin (B)=\sin (90)=1 \end{gathered}[/tex]
Now, we replace the values and solve for "A"
[tex]\begin{gathered} \frac{4}{\sin(A)}=\frac{12}{\sin(90)} \\ \sin (A)=\frac{4}{12}\cdot\sin (90) \\ A=\sin ^{-1}(\frac{4}{12}\cdot1) \\ A=19.47122\cong19.47 \end{gathered}[/tex]
In conclusion, the answer is approximately 19.47 degrees
