Final answer:
The height of the tree is calculated using proportions from the similar triangles formed by the person's height and shadow, and the tree's height and shadow. By setting up a proportion and cross-multiplying, the tree's height is found to be 52.2 feet.
Step-by-step explanation:
The question at hand is a classic example of solving proportions using similar triangles. In this scenario, the student's height and shadow form a right-angle triangle similar to the triangle formed by the tree's height and shadow. Since the triangles are similar, their corresponding sides are proportional, which can be expressed as:
Height of Student / Shadow of Student = Height of Tree / Shadow of Tree.
Using the given measurements, we can write:
5.8 feet / 3 feet = Height of Tree / 27 feet.
By cross-multiplying to solve for the tree's height, we get:
5.8 feet * 27 feet = Height of Tree * 3 feet.
Height of Tree = (5.8 feet * 27 feet) / 3 feet.
After doing the calculation, the Height of Tree is found to be 52.2 feet.