A 4-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow. How tall is the cell phone tower?
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Draw a diagram. Using similar triangles,
4/20 = x/125
To solve this problem, we can set up a proportion between the height of the post and the height of the cell phone tower using their respective shadows.
Let's denote the height of the cell phone tower as 'x'.
The proportion can be set up as:
(Height of the post) / (Shadow of the post) = (Height of the cell phone tower) / (Shadow of the cell phone tower)
Plugging in the given values:
4 ft / 20 in = x ft / 125 ft
To solve for 'x', we need to normalize the units.
First, we need to convert 20 inches to feet by dividing by 12 (since there are 12 inches in a foot):
4 ft / (20 in / 12 in/ft) = x ft / 125 ft
Simplifying:
4 ft / (20/12) = x ft / 125ft
4 ft / (5/3) = x ft / 125ft
4 ft * (3/5) = x ft * 1
12 ft / 5 = x ft
Therefore, the height of the cell phone tower is 12 ft * 5/1 = 60 ft.