Question

A 5' 6"-tall student casts a shadow 8 ft long at the same time a tree casts a 30-ft shadow. How tall is the tree? (Hint: The tree and its shadow are similar to the student and her shadow.)

A) 15 feet
B) 12 feet
C) 11.25 feet
D) 11 feet

Answer 1

The height of the tree is calculated using proportional relationships and is found to be 20.625 feet, based on the height of a 5' 6" tall student and their respective shadows.

Step-by-step explanation:

The question revolves around finding the height of a tree based on proportional relationships. Given that a 5' 6"-tall student casts an 8 ft long shadow and at the same time, a tree casts a 30-ft shadow, we can use the similarity in the triangles formed by the student and her shadow and the tree and its shadow to find the height of the tree.

First, we convert the student's height into feet: 5' 6" = 5.5 feet. Since the triangles are similar, the ratios of the sides are equal:

Student's height / Student's shadow length = Tree's height / Tree's shadow length

5.5 feet / 8 feet = Tree's height / 30 feet

Solving for the tree's height:

Tree's height = 5.5 feet × (30 feet / 8 feet)

Tree's height = (5.5 × 30) / 8

Tree's height = 165 / 8

Tree's height = 20.625 feet

Since this value is not in the options given, the student must have made a mistake in the available choices. The correct tree's height is 20.625 feet.