As you can see from the figure, it resembles a right-angled triangle.
Recall that the Pythagorean theorem is given by
[tex]c^2=a^2+b^2[/tex]Where a and b are the shorter sides and c is the longest side.
For the given case, the two shorter sides are known and the longest side is unknown that is the length of the connection.
First, convert the given lengths into a single unit.
[tex]\begin{gathered} 50\: ft\: 6\: in=50+\frac{6}{12}=50+0.5=50.5\: ft \\ 38\: ft\: 9\: in=38+\frac{9}{12}=38+0.75=38.75\: ft \end{gathered}[/tex]Now, substitute these values into the above formula
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=50.5^2+38.75^2 \\ c^2=2550.25+1501.5625 \\ c^2=4051.8125 \\ c=\sqrt[]{4051.8125} \\ c=63.65\: ft \end{gathered}[/tex]So, the length of the connection is
[tex]\begin{gathered} 63.65\: ft=0.65\times12=7.8=8\: in \\ 63\: ft\: 8\: in \end{gathered}[/tex]Therefore, the length of the connection is 63 ft 8 in
The angle above horizontal is given by
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]Where the opposite side is 38.75 ft and the adjacent side is 50.5 ft
[tex]\begin{gathered} \tan \theta=\frac{38.75}{50.5} \\ \theta=\tan ^{-1}(\frac{38.75}{50.5}) \\ \theta=37.5\degree \end{gathered}[/tex]Therefore, the angle above horizontal is 37.5°
