We have the following:
In this case the first thing is to calculate the value of the hypotenuse, by means of the cosine function.
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \theta=30 \\ \text{adjacent = 12} \end{gathered}[/tex]replacing:
[tex]\begin{gathered} \cos 30=\frac{12}{\text{hypotenuse}} \\ \text{hypotenuse}=12\cdot\cos 30=13.86 \end{gathered}[/tex]now, to calculate the side we use the Pythagorean theorem, as follows
[tex]\begin{gathered} c^2=a^2+b^2 \\ 13.86^2=12^2+b^2 \\ b^2=13.86-12^2 \\ b=6.94 \end{gathered}[/tex]Therefore, the area is:
[tex]\begin{gathered} A=\frac{12\cdot6.94}{2} \\ A=41.64 \end{gathered}[/tex]The area is 41.64 ft^2