Answer:
The height of the cell phone tower is 408 feet.
Step-by-step explanation:
This problem models a similarity between two right angles, one formed by the cell phone tower and its shadow, and the other formed by the vertical post and its shadow.
[tex]h_{1}[/tex] is the height of the cell phone tower.
[tex]h_{2}=4ft[/tex] represents the height of the vertical post.
[tex]s_{1}=119ft[/tex] represents the shadow of the cell phone tower.
[tex]s_{2}=14in=14in\frac{1ft}{12in}=\frac{7}{6} ft[/tex] represents the shadow of the vertical post.
Now, using the Thales theorem, we have
[tex]\frac{h_{1} }{h_{2} } =\frac{s_{1} }{s_{2} }\\ h_{1} =\frac{s_{1} }{s_{2} }h_{2}\\h_{1}=\frac{119ft}{\frac{7}{6}ft} (4ft)\\h_{1}=\frac{714}{7}(4)=102(4)=408ft[/tex]
Therefore, the height of the cell phone tower is 408 feet.
Remember that Thales' theorem is about the proportions derived from to parallels and its intersection with two transversal. The important part of this theorem is to apply in the right order, that is, the ratio between height and the ratio between shadows, it would be wrong if we use a ratio between height and shadows, it can cause confusion.
