From the given figure,
AB = Distance between Emily to a point of tangency.
BC = Radius of the pole
AC = Distance between Emily and the pole.
ABC is a right angled triangle at B.
Now,
[tex]\begin{gathered} In\text{ }\Delta ABC\text{ , By Using Pythagoras theorem } \\ AC^2=AB^2+BC^2 \end{gathered}[/tex]
Substituting the given values in the statement,
[tex]\begin{gathered} 24^2=12^2+r^2 \\ r^2=24^2-12^2 \\ r^2\text{ = }432 \\ r\text{ = 20.78 ft} \end{gathered}[/tex]
Thus the radius of the pole is 20.78 ft .
