A 4​-ft vertical post casts a 10​-in shadow at the same time a nearby cell phone tower casts a 120-ft shadow. How tall is the cell phone​ tower?

4 ft is 48 in

48 / 10 = x / 120 ft

10/12 = 5/6 Ft.

4/(5/6) = x/120
5x/6 = 480
X = 576 Ft.

864 ft.

its 600.

It's 576ft

Well, let's do some shadow math and tower-tallying! We have a 4-ft post casting a 10-in shadow and a mystical cell phone tower casting a 120-ft shadow. To find the height of the tower, we can set up a proportion: 4 ft is to 10 in as x is to 120 ft. Let's do some shuffling and cross multiplying! 4 ft multiplied by 120 ft equals 10 in multiplied by x. That equates to 480 ft = 10x in this twisted dimension. By dividing both sides by 10, we discover that x, the height of the cell phone tower, is a towering 48 feet! Isn't it funny how shadows can make things appear taller than they really are? The tower sure knows how to cast a long shadow!

To find the height of the cell phone tower, we can set up a proportion between the heights and the shadows.

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.