A maple tree casts a shadow of 45 ft long. At the same time, a 40-ft-long oak tree casts a shadow which is 60 ft long. Explain how you can use similar triangles to find the height of the tree. Then find the height of the tree.

Draw similar right triangles, one with sides of 40 and 60, and the other with sides of h and 45

Since the triangles are similar, the ratio of corresponding sides is constant.

h/40 = 45/60
h = 30

30/50

To use similar triangles to find the height of the tree, we need to understand the concept of proportions. Similar triangles are triangles that have the same shape but might be different in size. The ratios of the lengths of corresponding sides in similar triangles are equal.

Let's represent the height of the maple tree as "h" and its shadow length as "s". Similarly, for the oak tree, let's represent its height as "H" and its shadow length as "S". We can set up the following proportion based on the similar triangles formed by the trees and their shadows:

h/s = H/S

In this case, we can substitute the given values into the equation as follows:

h/45 = H/60

To solve for the height of the maple tree (h), we need to isolate it in the equation. We can cross-multiply to get:

h * 60 = 45 * H

Simplifying further:

60h = 45H

Now, we can solve for h by dividing both sides by 60:

h = (45H) / 60

Given that H (height of the oak tree) is 40 ft, we can substitute it into the equation:

h = (45 * 40) / 60

Calculating this:

h = 30 ft

Therefore, the height of the maple tree is 30 feet.