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?
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
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.
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
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.
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
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.