Questions: Question 4 of 10 A man is 6 feet tall. To find the height of a tree, the shadow of the man and the shadow of the tree were measured. The length of the man's shadow was 4 feet 6 inches. The length of the tree's shadow was 12 feet. What is the height of the tree? 15.7 ft 16 ft 32 ft 9 ft

Solution Steps

To find the height of the tree, we can use the concept of similar triangles. The ratio of the height of the man to the length of his shadow will be the same as the ratio of the height of the tree to the length of its shadow. We can set up a proportion and solve for the height of the tree.

The length of the man's shadow is given as \( 4 \) feet \( 6 \) inches. Converting this to feet: \[ \text{man\_shadow\_length} = 4 + \frac{6}{12} = 4.5 \text{ feet} \]

Using the concept of similar triangles, we set up the proportion: \[ \frac{\text{height of man}}{\text{length of man's shadow}} = \frac{\text{height of tree}}{\text{length of tree's shadow}} \] Substituting the known values: \[ \frac{6}{4.5} = \frac{h}{12} \]

Cross-multiplying gives: \[ 6 \cdot 12 = 4.5 \cdot h \] This simplifies to: \[ 72 = 4.5h \] Now, solving for \( h \): \[ h = \frac{72}{4.5} = 16 \text{ feet} \]

Final Answer