The length of the shadow would be the base of a triangle and the post/tower would be the height of a triangle.
We let the base of the triangle formed by the tower be [tex]b_t[/tex] and the height be [tex]h_t[/tex]. Similarly let the base of the triangle formed by the post be [tex]b_p[/tex] and the height be [tex]h_p[/tex].
[tex]\frac{h_t}{b_t}=\frac{h_p}{b_p}[/tex]
[tex]\frac{h_t}{100}=\frac{5}{12}[/tex]
[tex]12h_t=500[/tex]
[tex]h_t=\frac{500}{12}=\frac{125}{3}[/tex]
