4 ft is 48 in
48 / 10 = x / 120 ft
48 / 10 = x / 120 ft
4/(5/6) = x/120
5x/6 = 480
X = 576 Ft.
Let's first convert the units to the same system. Since the post's height is given in feet and the shadow is given in inches, let's convert the shadow of the post to feet:
Shadow of the post = 10 inches = 10/12 feet = 5/6 feet
Now we can set up the proportion:
(Post height) / (Shadow of the post) = (Cell phone tower height) / (Shadow of the cell phone tower)
Let's plug in the values:
4 feet / (5/6 feet) = (Cell phone tower height) / 120 feet
To solve for the cell phone tower height, we cross-multiply and then solve for the unknown:
4 feet * 120 feet = (5/6 feet) * (Cell phone tower height)
480 feet = (5/6 feet) * (Cell phone tower height)
To isolate the Cell phone tower height, we can divide both sides of the equation by (5/6 feet):
(Cell phone tower height) = (480 feet) / (5/6 feet)
To divide by a fraction, we can multiply by its reciprocal:
(Cell phone tower height) = (480 feet) * (6/5 feet)
Now, let's calculate it:
(Cell phone tower height) = 576 feet
Therefore, the height of the cell phone tower is 576 feet.