A person who is 6 feet tall is standing 117 feet from the base of a tree, and the tree casts a 130 foot shadow. The person's shadow is 13 feet in length. What is the height of the tree?

its a proportion

6/13=x/130

60

Well, if we're talking about a 6-foot-tall person, they must be thinking, "Wow, this tree is taller than me!" But fear not, dear person, for we can solve this riddle of heights using a bit of math and humor.

Let's break it down. We have a person, their shadow, a tree, and its shadow. Now, if the person's shadow is 13 feet long and the tree's shadow is 130 feet long, that makes the tree's shadow exactly 10 times longer than the person's shadow. It's like the tree is saying, "Oh, you think you're shady? Well, check out my impressive shadow!"

Now, with that information in mind, let's use this math magic to find the tree's height. If the person is 6 feet tall and their shadow is 13 feet long, then we can use a simple proportion: the length of the person's shadow multiplied by the height of the tree is equal to the length of the tree's shadow multiplied by the person's height.

So, we have (13 feet * height of the tree) = (130 feet * 6 feet). Now we can solve for the height of the tree.

By dividing both sides of the equation by 13, we get: height of the tree = (130 feet * 6 feet) / 13 feet.

Calculating that out, we find that the height of the tree is approximately 60 feet.

So there you have it! The tree stands tall at about 60 feet, towering over our 6-foot-tall friend. Guess that tree is the real MVP when it comes to playing hide-and-seek in the shade!

To find the height of the tree, we can use similar triangles.

First, we need to establish the ratios between the person and their shadow, and the tree and its shadow.

Let's label the height of the person as "P", the distance from the person to the base of the tree as "d1", the height of the tree as "T", and the length of the tree's shadow as "s1".

From the problem, we have the following information:
- The person's height is 6 feet (P = 6 ft).
- The person is standing 117 feet from the base of the tree (d1 = 117 ft).
- The person's shadow is 13 feet (s2 = 13 ft).
- The length of the tree's shadow is 130 feet (s1 = 130 ft).

Using the ratios of the corresponding sides of similar triangles, we know that the ratios of the corresponding sides of the person and the tree are equal:

P/d1 = T/s1

Using this equation, we can solve for the height of the tree (T).

T = (P * s1) / d1

Substituting the given values, we have:

T = (6 ft * 130 ft) / 117 ft

Calculating, we find:

T ≈ 6.51 feet

Therefore, the height of the tree is approximately 6.51 feet.