13.2 cm
Explanation
as the tangent line is perpendicular to the radius, we have a rigth triangle, so we can unse Pythagorean Theorem
it says: for a rigth triangle
[tex]\text{side}1^2+side2^2=hypotenuse^2[/tex]
then
Let
side1=15
side2= unknown
hypotenuse=20
now, replace,
[tex]\begin{gathered} \text{side}1^2+side2^2=hypotenuse^2 \\ 15^2+side2^2=20^2 \\ 225+side2^2=400 \\ \text{subtract 225 in both sides} \\ 225+side2^2-225=400-225 \\ side2^2=175 \\ \text{side}2=\sqrt[]{175} \\ \text{side}2=13.228 \\ \text{rounded } \\ \text{side}2=13.2 \end{gathered}[/tex]
so, the answer is 13.2 cm.
i hope this helps you
