θ = 64°
Explanation:Trigonometric ratio SOHCAHTOA
hypotenuse = 10cm
angle = θ
opposite = side opposite the angle = 9cm
adjacent = not given
Since we know the opposite and the hypotenuse, we would apply sine ratio (SOH)
[tex]\begin{gathered} \sin \text{ }\theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin \text{ }\theta\text{ = }\frac{9}{10} \end{gathered}[/tex][tex]\begin{gathered} \sin \theta\text{ = 0.9} \\ \theta=sin^{-1}(0.9) \\ \theta=\text{ 64.16}\degree \\ To\text{ the nearest degr}ee,\text{ }\theta=\text{ 64}\degree \end{gathered}[/tex]
