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Determine the acute angle, \(\theta\), given the trigonometric ratio. Round to the nearest degree.

1. \(\sin \theta = \frac{3}{5}\)
   
   
   Solution

   \(\begin{align}
    \sin \theta &= \frac{3}{5} \\
    \theta &= \sin ^{-1} \left( {\frac{3}{5}} \right) \\
    \theta &= 36.869...^\circ  \\
    \theta &\doteq 37^\circ  \\
    \end{align}\)
   
   
   
   
2. \(\cos \theta = 0.1736\)
   
   
   Solution

   \(\begin{align}
    \cos \theta &= 0.1736 \\
    \theta &= \cos^{-1} \left( {0.1736} \right) \\
    \theta &= 80.002...^\circ  \\
    \theta &\doteq 80^\circ  \\
    \end{align}\)