A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow. How tall is the cell phone tower?
use simple ratio ... notice the mix of units
2/(20/12) = x/125
6/5 = x/125
solve for x
approximately :)
the Correct answer is 144
Well, it seems like the post and the cell phone tower got into a bit of a shadow competition! Let's see who takes the crown for tallest shadow.
First, let's compare the lengths of the shadows. We have a 2-ft post with a 20-in shadow, and a mysterious cell phone tower with a 125-ft shadow.
Now, to find the height of the cell phone tower, we can set up a proportion. If we assume the height of the cell phone tower is 'x', we can set up the following equation:
2 ft / 20 in = x ft / 125 ft
To solve this proportion, we need to convert everything to the same units. Let's convert inches into feet:
20 in = 20/12 ft = 5/3 ft
Now our proportion becomes:
2 ft / (5/3 ft) = x ft / 125 ft
Simplifying the proportion, we get:
(2/1) / (5/3) = x / 125
Cross-multiplying, we get:
6 = (5/3) * x
To solve for x, we multiply both sides of the equation by (3/5):
6 * (3/5) = x
And voilà! We find that the height of the cell phone tower is approximately 18 feet. So, the cell phone tower stands tall at 18 feet, casting its extensive 125-ft shadow.
To find the height of the cell phone tower, we need to use similar triangles. Similar triangles have corresponding angles that are equal and proportional side lengths.
Let's label the height of the post as x and the height of the cell phone tower as h. We also know that the post casts a 20-in shadow, and the cell phone tower casts a 125-ft shadow.
Using the respective heights and shadows, we can set up the following proportion:
\( \frac{{\text{{Height of the post}}}}{{\text{{Height of the shadow of the post}}}} = \frac{{\text{{Height of the cell phone tower}}}}{{\text{{Height of the shadow of the cell phone tower}}}} \)
\( \frac{{x}}{{20\,in}} = \frac{{h}}{{125\,ft}} \)
Now, let's convert both measurements to the same unit (inches or feet) to solve for h:
1 foot = 12 inches, so 125 feet = 125 × 12 = 1500 inches.
The equation becomes:
\( \frac{{x}}{{20\,in}} = \frac{{h}}{{1500\,in}} \)
To solve for h, we can cross-multiply:
\( x \times 1500 = 20 \times h \)
Now, we can solve for h:
\( h = \frac{{x \times 1500}}{{20}} \)
Since we know that the height of the post is 2 feet, we can substitute x = 2 into the equation:
\( h = \frac{{2 \times 1500}}{{20}} \)
Calculating the value of h gives us:
\( h = 150 \) feet.
Therefore, the cell phone tower is 150 feet tall.