Answer :

We have

RT is the diameter

mSO=10

In order to find SA, we will use a trigonometric function

[tex]\begin{gathered} \sin (30)=\frac{SA}{10} \\ SA=\sin (30)\cdot10=5 \end{gathered}[/tex]

SM is double of SA

[tex]SM=2(5)=10[/tex]

Then using the Pythagorean theorem

[tex]\begin{gathered} OA=\sqrt[]{OS^2-SA^2} \\ OA=\sqrt[]{10^2-(5)^2}=5\sqrt[]{3} \end{gathered}[/tex]

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