Question

the height of an object varies directly with the length of its shadow. a person 6ft tall casts a 8.5ft shadow, while a tree casts a 38ft shadow. how tall is the tree

Answer 1

The answer to your question is Tree's height = 26.8 ft

Explanation:

Data

Person Tree

height = 6 ft height = x

shadow = 8.5 ft shadow = 38 ft

Process

1.- Use the Thales' theorem to solve this problem

Person's height/ Person's shadow = Tree´s height / Tree's shadow

Solve for Tree's height

Tree's height = Person's height x Tree's shadow / Person's shadow

Substitution

Tree's height = 6 x 38 / 8.5

Simplification

Tree's height = 228 / 8.5

Result

Tree's height = 26.8 ft