A tree casts a shadow that is 20 feet long. A 5-foot-tall boy stands in the shadow so that the end of his shadow lines up with that of the tree. His shadow is 6 feet long. How tall is the tree
Cross multiply and solve for x.
x/20 = 5/6
The answer is not 20 feet, it is 50/3 or 16.7
To determine the height of the tree, we need to use similar triangles. Let's set up a proportion:
Height of the tree / Length of the tree's shadow = Height of the boy / Length of the boy's shadow
Let's substitute the given values into the proportion:
Height of the tree / 20 feet = 5 feet / 6 feet
To solve for the height of the tree, we can cross-multiply and then divide:
Height of the tree = (5 feet / 6 feet) * 20 feet
Height of the tree = (5/6) * 20 feet
Height of the tree = 100/6 feet
Simplifying the fraction:
Height of the tree ≈ 16.67 feet
Therefore, the approximate height of the tree is 16.67 feet.