A student wants to determine the height of a tree. She knows that her six foot tall Teacher cast a 10 foot long shadow at the same time that the tree has a 45 foot long shadow. How tall is the tree?

Cross multiply and solve this proportion for x.

6/10 = x/45

x=27

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

Step 1: Set up a proportion between the height of the teacher and the length of the teacher's shadow, and the height of the tree and the length of the tree's shadow.

The proportion is as follows:
Teacher's height / Teacher's shadow length = Tree's height / Tree's shadow length

Step 2: Substitute the known values into the proportion.

The teacher's height is 6 feet, and the teacher's shadow is 10 feet. The tree's shadow is 45 feet.

6 / 10 = Tree's height / 45

Step 3: Cross-multiply and solve for the unknown height of the tree.

(6 * 45) / 10 = Tree's height

270 / 10 = Tree's height

27 = Tree's height

Therefore, the height of the tree is 27 feet.

To determine the height of the tree, you can set up a proportion using the measurements given. Let's label the height of the tree as "h".

We know that the teacher's height is 6 feet and the length of the teacher's shadow is 10 feet. Similarly, we know that the length of the tree's shadow is 45 feet.

We can set up the proportion as follows:

(height of the teacher) / (length of the teacher's shadow) = (height of the tree) / (length of the tree's shadow)

6 feet / 10 feet = h / 45 feet

To solve for "h" which represents the height of the tree, we can cross-multiply and then solve for "h":

6 feet * 45 feet = 10 feet * h

270 feet = 10 feet * h

Dividing both sides of the equation by 10 feet:

270 feet / 10 feet = h

27 feet = h

Therefore, the height of the tree is 27 feet.