Use similar triangles to solve. A person who is 6 feet tall is standing 108 feet from the base of a​ tree, and the tree casts a 120 foot shadow. The​ person's shadow is 12 feet in length. What is the height of the​ tree?

Using similar triangles,

h/(108+12) = 6/12

60'

In such many ways

Why did the tree go to math class? Because it wanted to branch out and solve some problems, of course! Let's get cracking on this one.

We have a person who is 6 feet tall and is 108 feet away from the tree. The person's shadow is 12 feet long, while the tree's shadow is 120 feet long.

So, we can set up the following proportion:

(person's height) / (person's shadow) = (tree's height) / (tree's shadow)

Plugging in the values we know:

6 / 12 = (tree's height) / 120

Now, let's cross-multiply and solve for the tree's height:

12 * (tree's height) = 6 * 120

(tree's height) = (6 * 120) / 12

(tree's height) = 60 feet

So, using similar triangles, we can determine that the height of the tree is 60 feet. Now that's some tall timber!

To solve this problem using similar triangles, we need to identify the corresponding sides of the triangles formed by the person, the tree, and their respective shadows.

Let's label the height of the person as "x" (in feet) and the height of the tree as "h" (in feet).

We have two similar triangles: the triangle formed by the person and their shadow, and the triangle formed by the tree and its shadow.

In the triangle formed by the person and their shadow, we have the following sides:
- The person's height (x feet)
- The person's shadow length (12 feet)

In the triangle formed by the tree and its shadow, we have the following sides:
- The tree's height (h feet)
- The tree's shadow length (120 feet)

Since the two triangles are similar, we can set up the following proportion:

(person's height) / (person's shadow length) = (tree's height) / (tree's shadow length)

x / 12 = h / 120

Now, we can solve for "h" by cross-multiplying:

x * 120 = 12 * h

120x = 12h

To isolate "h," divide both sides of the equation by 12:

h = (120x) / 12

Simplifying further:

h = 10x

Therefore, the height of the tree is 10 times the height of the person.