Question 4.4.7: James McIntosh wants to cut down a tree in his front yard, b......
James McIntosh wants to cut down a tree in his front yard, but he is worried about it falling into his garage. He needs to know the height of the tree. One morning, he notices that his own 6-foot body casts an 8-foot shadow at the same time that a typical tree casts a 34-foot shadow. Find the height of the tree.
Step-by-Step
Set up a proportion in which the height of the tree is given the variable name x.
\frac{6}{8} = \frac{x}{34}
6 • 34 = 8 • x Cross multiply.
\frac{204}{8} = \frac{\cancel{8}\ •\ x}{\cancel{8}} Divide by 8.
x = 25.5 feet
The height of the tree is 25.5 feet.
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