An Actual Application of the Law of Sines

I have the privilege of teaching an algebra and trigonometry class for engineering tech students.  I am always looking for ways to help my students experience the relevance of a concept.  My parents' DIY patio project this past weekend provided an awesome practical application of the Law of Sines.

My mom wanted some shade around the pool so she found the photo below online and tasked my dad and brother-in-law with making it happen.

They were cruising along until I received the following picture from my mom:

They were wanting to figure out the exact angle to cut the front diagonal boards (near the peak) without a few hours of guess and check.  They did know that they wanted the length of the diagonal board to be 30 inches.  She also sent me a quick sketch:

I observed that it would be close to an isosceles triangle, but my brother-in-law is a perfectionist so I used the Law of Sines to give him 4 decimal places.  Here was my work:

The angles worked great and I did a happy dance because I am so excited to use this scenario with my students.  Would you have solved it differently?