Question

A 6​-ft vertical post casts a 20​-in shadow at the same time a nearby cell phone tower casts a 115​-ft shadow. How tall is the cell phone​ tower?

Answer 1

i figured out this proportion 6/20=115/x multiplied and i keep getting 383.333 repeating when it should come out to be 414 ft

Answer 2

You have to have both fractions following the same pattern

You started with 6/20 which is vertical in feet over shadow length in inches

so you should have
72/20 = x/1380 , noticed I changed all units to inches, and my numerators are verticals and the denominators are horizontals.
20x = 99360
x = 1380/20 = 4968 inches or 414 ft

Answer 3

6/20 is height/shadow

So, your proportion should be
6/20 = x/115
x = 34.5

You did not do a sanity check on either of your solutions.
The post is about 1/3 as big as its shadow.
So, the tower should be about 1/3 as big as its shadow.

Answer 4

oops. Go with Reiny. I neglected the units.

Answer 5

20in * 1ft/12in = 20/12 = 5/3 Ft.

6/(5/3) = y/115.
Multiply both sides by 115:
Y = 690/(5/3) = 414 Ft. = Ht. of tower.

Answer 6

all of the response could have been simplified because i am looking for help on my homework the mathxl website keeps saying its wrong so try simplifying it next time thanks

Answer 7

[AI-generated answer — Explain Bot]

To find the height of the cell phone tower, we can set up a proportion using the information given.

We have the following information:
For the vertical post:
Height = 6 ft
Shadow length = 20 in

For the cell phone tower:
Shadow length = 115 ft

We can set up a proportion using the height and shadow lengths:
(height of vertical post) / (shadow length of vertical post) = (height of cell phone tower) / (shadow length of cell phone tower)

Substituting the given values:
6 ft / 20 in = (height of cell phone tower) / 115 ft

Now we need to convert the units so that they match. Let's convert 6 ft to inches:
6 ft = 6 ft * 12 in/ft = 72 in

So, substituting the values again:
72 in / 20 in = (height of cell phone tower) / 115 ft

To solve for the height of the cell phone tower, we cross multiply and then divide:
(72 in * 115 ft) / 20 in = height of cell phone tower

Now let's solve the calculation:
8280 in ft / 20 in = height of cell phone tower

Canceling out the units:
414 ft = height of cell phone tower

Therefore, the cell phone tower is 414 feet tall.