The height of the tree is 108 inches.
Solving the Similar Triangle Application Problem
Given:
Bill's height = 6 feet
Length of Bill's shadow = 9 feet
Distance Bill walks along the tree's shadow = 24 feet
Length of the tree's shadow = x feet
Identify similar triangles:
Triangle formed by the tree and its shadow is similar to triangle formed by Bill and his shadow.
Set up proportions:
Since the triangles are similar, we can set up proportions:
h/x = 6/9
Solve for x:
Cross-multiply and solve for x:
h = 6 * x/9
x = 9h/6
Substitute known values and solve for h:
Replace h with Bill's height:
x = 9 * 6 / 6
x = 9
Therefore, the height of the tree is 9 feet.
Rounding to inches:
9 feet is equal to 9 * 12 inches = 108 inches.