If a person standing 5 feet tall casts a shadow 12 feet long, then how long is a tree's shadow if a tree stands 17.5 feet tall?
x=shadow length
12/x=5/12
5/12=0.417
12/x=0.417
12/0.416=28.8ft
check:12/28.8=0.417
28.8ft
the ratio of shadow/height is constant, so
12/5 = x/17.5
or, the height and shadow scale the same way, so since 17.5 is 3.5 times 5, the shadow will be 3.5 times 12 feet long.
got me numbers mixed up, sorry
replace 12 with 17.5
To determine the length of the tree's shadow, you can use the concept of similar triangles. Similar triangles have proportional sides, which means that the ratio of corresponding sides is equal.
Let's set up a proportion using the given information:
The height of the person is 5 feet, and the length of their shadow is 12 feet.
The height of the tree is 17.5 feet, and we need to find the length of its shadow.
We can set up the proportion:
(person's height) / (person's shadow length) = (tree's height) / (tree's shadow length)
Substituting the values we know:
5 / 12 = 17.5 / x, where x represents the length of the tree's shadow.
To find x, we can cross multiply and then solve for x:
5x = 12 * 17.5
Multiply the values on the right side:
5x = 210
Divide both sides by 5:
x = 210 / 5
Simplifying:
x = 42
Therefore, the length of the tree's shadow is 42 feet.