Consider the formulae from Inverse Trigonometry,
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Hypotenuse}}) \\ \theta=\tan ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Adjacent Leg}}) \\ \theta=\cos ^{-1}(\frac{\text{ Adjacent Leg}}{\text{ Hypotenuse}}) \end{gathered}[/tex]
Solve for the first angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.139) \\ \theta\approx82^{\circ} \end{gathered}[/tex]
Thus, the required angle measure is 82 degrees approximately.
Solve for the second angle as,
[tex]\begin{gathered} \theta=\tan ^{-1}(0.249) \\ \theta\approx14^{\circ} \end{gathered}[/tex]
Thus, the required angle measure is 14 degrees approximately.
Solve for the third angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.469) \\ \theta\approx28^{\circ} \end{gathered}[/tex]
Thus, the required angle measure is 28degrees approximately.
Solve for the fourth angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.682) \\ \theta\approx47^{\circ} \end{gathered}[/tex]
Thus, the required angle measure is 47 degrees approximately.
Solve for the fifth angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.848) \\ \theta\approx58^{\circ} \end{gathered}[/tex]
Thus, the required angle measure is 58 degrees approximately.
