Apply the sine rule in triangle RST,
[tex]\frac{ST}{\sin R}=\frac{RS}{\sin T}=\frac{TR}{\sin S}[/tex]Substitute the values,
[tex]\frac{ST}{\sin39}=\frac{RS}{\sin90}=\frac{55}{\sin S}[/tex]We know that the sum of all angles of a triangle is 180 degrees,
[tex]\angle R+\angle S+\angle T=180\Rightarrow39+\angle S+90=180\Rightarrow\angle S=51[/tex]Substitute this value,
[tex]\frac{ST}{\sin39}=\frac{RS}{\sin90}=\frac{55}{\sin51}\Rightarrow ST=\sin 39\times\frac{55}{\sin51}\Rightarrow ST\approx44.5[/tex]Thus, the length of side ST is 44.5 feet approximately.
