Diane is 5’8” tall and wants to find the height of an oak tree in her front yard

Question

Diane is 5’8” tall and wants to find the height of an oak tree in her front yard. She walks along with the shadow of the tree until her head is in a position where the end of her shadow exactly overlaps the end of the treetop’s shadow. She is now 11’3” from the foot of the tree and 8’6” from the end of the shadow. How tall is her oak tree?

Answer 1

5'8 = 5 2/3 feet = 17/3 ft

8'6 = 8.5 feet = 17/2 ft

11'3 + 8'6 = 19'9 = 19 3/4 = 79/4 ft

h/79/4 = 17/2/17/3 = 2/3

h = (79/4)(2/3) = 79/6 = 13 1/6 = 13'2

height = 13 feet 2 inches

Answer 2

Draw and label a diagram

h represents the height of the tree

By similar figures

h / (11' 3" + 8' 6") = 5' 8" / 8' 6"

Can you solve for h and answer?