Height of a Tree A woodcutter determines the height of a tall tree by first measuring a smaller one 125 ft away, then moving so that his eyes are in the line of sight along the tops of the trees and measuring how far he is standing from the small tree (see the figure). Suppose the small tree is 20 ft tall, the man is 25 ft from the small tree, and his eye level is 5 ft above the ground. How tall is the taller tree?
Height of a Tree A woodcutter determines the height of a tall tree by first measuring a smaller one 125 ft away, then moving so that his eyes are in the line of sight along the tops of the trees and measuring how far he is standing from the small tree (see the figure). Suppose the small tree is 20 ft tall, the man is 25 ft from the small tree, and his eye level is 5 ft above the ground. How tall is the taller tree?
Height of a Tree A woodcutter determines the height of a tall tree by first measuring a smaller one 125 ft away, then moving so that his eyes are in the line of sight along the tops of the trees and measuring how far he is standing from the small tree (see the figure). Suppose the small tree is 20 ft tall, the man is 25 ft from the small tree, and his eye level is 5 ft above the ground. How tall is the taller tree?
Expert Solution & Answer
To determine
To find: The height of taller tree.
Answer to Problem 52E
The height of taller tree is 95 ft.
Explanation of Solution
Given:
The distance between taller tree and smaller tree is 125 ft.
The height of man is 5ft and the height of smaller tree is 20 ft.
Distance between man and smaller tree is 25 ft.
Calculation:
Let the height of taller tree be x. For a pair of similar triangles the ratios of corresponding sides are equal.
Tabulate the given information into the language of algebra.
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