I am 5'2 and cast a shadow 3' long. My friend casts a shadow 3' 5" long. How tall is he?
use a proportion:
62"/36"=h/43"
the trick here is the units, get them common units,no mixed units.
5 2/12 ** x
------ = --------
**3*** ** 3 5/12
3 x = (31/6)(41/12)
x = 5.88 feet or 5 feet 10 1/2 inches
Convert to inches, then use a ratio.
5'2' = 62"
3' = 36"
3'5" = 41"
62:36 = x:41
62/36 = x:41
Cross multiply and solve for x.
To determine how tall your friend is based on the length of their shadow, we can use a proportion. Let's set up the proportion using the height and shadow length ratios.
First, convert the height of the shadows to the same unit of measurement. In this case, let's convert the 3' 5" shadow length to feet. Since 1 foot is equal to 12 inches, there are 12 inches in a foot. So, 5 inches is equal to 5/12 feet.
Now, we have the following proportions:
Your height: 5'2"
Your shadow length: 3'
Friend's shadow length: 3' + 5/12'
Height ratio: Your height / Friend's height
Shadow length ratio: Your shadow length / Friend's shadow length
Plugging the values into the equation:
(5'2" / Friend's height) = (3' / (3' + 5/12'))
To simplify the equation, we need to convert the heights to a consistent format, in this case, inches. There are 12 inches in a foot. So, your height is 5 feet + 2 inches = 62 inches.
Let's solve the equation:
(62 / Friend's height) = (36 / (36 + (5/12)))
To cross-multiply and solve for Friend's height, we have:
62 * (36 + (5/12)) = 36 * Friend's height
Now, calculate the left side of the equation:
(62 * (36 + (5/12))) = 2415.83
Therefore, 2415.83 = 36 * Friend's height
Now, solve for Friend's height:
2415.83 / 36 = Friend's height
Friend's height ≈ 67.11 inches.
Converting inches to feet and inches, Friend's height is approximately 5 feet 7 inches.
So, your friend is approximately 5 feet 7 inches tall.