Man 6 feet tall cast shadow 15 ft long. Girl is 5 ft. 10 inches how long will her shadow be
Use a proportion. Cross multiply and solve for x.
6/15 = (5 5/6)/x
5x = 6 * (35/6)
5x = 35
x = 35/5
x = ?
To determine the length of the girl's shadow, we can use the concept of similar triangles. The length of the man's shadow and the man's height form one set of corresponding sides of two similar triangles. We can then use this proportion to find the length of the girl's shadow.
Let's set up the proportion:
(man's shadow length) / (man's height) = (girl's shadow length) / (girl's height)
Now, let's substitute the values we have:
15 ft / 6 ft = (girl's shadow length) / (5 ft 10 in)
To convert the girl's height to feet, we need to convert 10 inches to feet. Since 12 inches equal 1 foot, 10 inches would be 10/12 = 5/6 feet.
Substituting this value:
15 ft / 6 ft = (girl's shadow length) / (5.833 ft)
To find the girl's shadow length, we can cross-multiply:
(15 ft) * (5.833 ft) = (6 ft) * (girl's shadow length)
The product on the left side represents the length of the girl's shadow:
87.495 ft = (6 ft) * (girl's shadow length)
Now, we can solve for the girl's shadow length:
girl's shadow length = 87.495 ft / 6 ft
Calculating this division:
girl's shadow length ≈ 14.58 ft
Therefore, the girl's shadow will be approximately 14.58 feet long.