If a tree cast a shadow 30 feet long at the same time that a boy 5 feet tall cast a shadow 3 long. Find the height in feet of the tree.

Set up a proportion, cross multiply, and solve for x.

x/30 = 5/3

To find the height of the tree, we can use the concept of similar triangles. In this case, the height of the tree can be represented by the ratio of its shadow length to the boy's shadow length.

Let "h" be the height of the tree.

The ratio of the tree's shadow length to the boy's shadow length is:

(tree's shadow length) / (boy's shadow length) = h / 5

Given that the tree's shadow length is 30 feet and the boy's shadow length is 3 feet, we can write the equation as:

30 / 3 = h / 5

Simplifying the equation:

10 = h / 5

Multiply both sides of the equation by 5 to solve for "h":

5 * 10 = h

Therefore, the height of the tree is 50 feet.

To find the height of the tree, we can use a proportion comparing the length of the tree's shadow to the height of the tree, and the length of the boy's shadow to the height of the boy.

Let's denote the height of the tree as 'x'.

According to the information given:
Length of the tree's shadow = 30 feet
Length of the boy's shadow = 3 feet
Height of the boy = 5 feet

We can set up the proportion:

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

Substituting the values:
30 / x = 3 / 5

To solve for 'x', we can cross-multiply:
30 * 5 = 3 * x

150 = 3x

Now, divide both sides by 3:
150 / 3 = x

x = 50

Hence, the height of the tree is 50 feet.

68