if a person is 6 feet tall and casts a 9 foot shadow, how tall would the shadow of a 100 foot tall tree be?

or using proportions and cross multiply:

6:9
100:?
? = 100*9/6=150

A tree and a building stand side by side. The 5-foot tall tree casts a shadow of 12 feet. If the building is 80 feet tall, how long is its shadow?

To determine the height of the shadow cast by a 100-foot tall tree, we can use the ratio between the height of the person, the length of their shadow, and the height of the tree.

First, let's understand the ratio between the height of the person and the length of their shadow. In this case, the person is 6 feet tall and their shadow is 9 feet long. This can be expressed as:

Height of person: Length of shadow = 6 feet : 9 feet

To find the ratio, we divide both sides of the equation by a common factor, in this case, 3 feet:

Height of person: Length of shadow = 2 feet : 3 feet

Now, we can use this ratio to determine the height of the shadow cast by the 100-foot tall tree.

Since the person's height and shadow length have a ratio of 2:3, we can assume that the tree's height and its shadow length will also have the same ratio. Applying the ratio to the height of the tree:

Height of person: Length of shadow = 2 feet : 3 feet
Height of tree: Length of shadow (unknown)

Given that the tree is 100 feet tall, we can set up a proportion:

2 feet / 3 feet = 100 feet / x feet

Simplifying the equation:

2/3 = 100 / x

To solve for x, we can cross-multiply:

2x = 3 * 100
2x = 300

Dividing both sides by 2:

x = 300 / 2
x = 150 feet

So, the shadow cast by the 100-foot tall tree would be 150 feet long.

6 / 9 = 100 / x Multiply both sides with x

6 x / 9 = 100 Multiply both sides with 9

6 x = 9 * 100

6 x = 900 Divide both sides with 6ž

x = 900 / 6

x = 150 ft

OR

9 / 6 = 1.5

x / 100 = 1.5 Multiply both sides with 100

x = 1.5 * 100

x = 150 ft