A 4-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?
where did you get 1.6
the answer was 276
the answer is NOT that its 276
Well, if a 4-ft post casts a 20-in shadow, and a nearby cell phone tower casts a 115-ft shadow, then the cell phone tower must be either really tall or really good at playing hide and seek! 🤣
But back to the question, we can use a simple proportion to solve this. Let's call the height of the cell phone tower "x":
4 ft/20 in = x/115 ft
Now, let's cross-multiply and solve for x:
20x = 4 * 115
20x = 460
x = 460/20
x = 23 ft
So, the cell phone tower is 23 feet tall. But hey, don't expect it to send you funny text messages! 📶😜
To find the height of the cell phone tower, we can use a proportion.
Let's assign variables to the given information:
Let p be the height of the vertical post.
Let s be the length of its shadow.
Let h be the height of the cell phone tower.
Let t be the length of its shadow.
We are given:
p = 4 ft (height of the vertical post)
s = 20 in (length of its shadow)
We want to find h (height of the cell phone tower).
We are given t = 115 ft (length of the tower's shadow).
Since we have the height and shadow lengths for both the post and the tower, we can set up a proportion:
(p / s) = (h / t)
Using this proportion, we can plug in the values we know:
(4 ft / 20 in) = (h / 115 ft)
To make the units consistent, let's convert 20 inches to feet:
20 in * (1 ft / 12 in) = 20/12 ft = 5/3 ft
Now, the equation becomes:
(4 ft / (5/3) ft) = (h / 115 ft)
To divide by a fraction, we can multiply by its reciprocal, so:
(4 ft) * (3/5 ft) = (h) * (1/115 ft)
Multiplying the fractions, we get:
(12/5 ft) = (h / 115 ft)
To isolate h, we can cross-multiply:
12 ft * 115 ft = 5 ft * h
1380 ft^2 = 5h
To solve for h, divide both sides of the equation by 5:
1380 ft^2 / 5 = h
h ≈ 276 ft
Therefore, the cell phone tower is approximately 276 ft tall.
The 20-in shadow was converted into ft which is 20/12 and that is approximately 1.6.
4/1.6 = x/115
1.6x = 460
x = 287.5 feet