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/17.5 = 12/5
Solve for x.
To find the length of the tree's shadow, you can use the concept of similar triangles. Similar triangles have the same shape but different sizes. In this case, we have two similar right-angled triangles: one with the person and their shadow, and the other with the tree and its shadow.
Let's set up proportions to solve for the length of the tree's shadow.
First, let's assign variables to the given measurements:
- Height of the person (h1) = 5 feet
- Length of the person's shadow (s1) = 12 feet
- Height of the tree (h2) = 17.5 feet
- Length of the tree's shadow (s2) = to be determined
We can set up the proportion:
h1 / s1 = h2 / s2
Plugging in the given values:
5 / 12 = 17.5 / s2
To solve for s2 (the length of the tree's shadow), we need to cross-multiply and then divide:
5s2 = 12 * 17.5
Next, we divide both sides by 5:
s2 = (12 * 17.5) / 5
Using a calculator:
s2 = 210 / 5
Therefore, the length of the tree's shadow is 42 feet.