I HAVE MY MOCKS TOMORROW AND I WILL DO THE SAME TEST THAT I HAVE KNOW HEEEEELP

Answer:[tex]p=\frac{4\sqrt{10}}{5}[/tex]  Step-by-step explanation:step 1Find the radius of the circleRemember that AB is a tangent to the circle at point BsoAB is perpendicular to OAThe radius of the circle is equal to the segment OAIn the right triangle OAB[tex]sin(30\°)=\frac{OA}{OB}[/tex][tex]OA=(OB)sin(30\°)[/tex]substitute the values[tex]OA=(16)0.5=8\ units[/tex]step 2Find the value of pIn the right triangle OPQsee the attached figure to better understand the problemApplying the Pythagoras Theorem[tex]OP^2=OQ^2+PQ^2[/tex]substitute the valuesRemember that OP is the radius[tex]8^2=p^2+(3p)^2[/tex][tex]64=p^2+9p^2[/tex][tex]64=10p^2[/tex][tex]p^2=\frac{64}{10}[/tex][tex]p=\frac{8}{\sqrt{10}}[/tex]simplify[tex]p=\frac{4\sqrt{10}}{5}[/tex]