joni notices that a 15 ft. flag pole cast a shadow of 25 feet. A tree next to the flag pole cast as shadow of 85 feet. how tall is the tree?

Set up a proportionality

15/25=x/85
original/shadow for each

x=51 ft

To find the height of the tree, we need to use proportions.

A proportion is an equation that states that two ratios are equal. In this case, we can set up a proportion with the lengths of the flag pole and its shadow, and the lengths of the tree and its shadow.

Let's assume the height of the tree is "x".

The proportion we can set up is:

Height of flag pole / Length of flag pole shadow = Height of tree / Length of tree shadow

Using the given information, we can substitute the values into the proportion:

15 ft / 25 ft = x / 85 ft

To solve for "x", we can cross-multiply and solve the equation:

15 ft * 85 ft = 25 ft * x

1275 ft² = 25 ft * x

Dividing both sides of the equation by 25 ft, we find:

x = 1275 ft² / 25 ft

Simplifying the division gives us:

x ≈ 51 ft

Therefore, the tree is approximately 51 feet tall.