Math Problem Statement
A pole 33 m tall casts a shadow 44 m long. A nearby tree casts a 1515 m shadow as shown in the diagram.
What is the height of the tree?
A.8.328.32 m
B.11.2511.25 m
C.13.0013.00 m
D.21.0221.02 m
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Solution
To solve this problem, we can use similar triangles. The pole and the tree, along with their shadows, form two right-angled triangles. Since both the pole and the tree are standing in the same sunlight, the angle of elevation of the sun is the same for both, meaning their triangles are similar.
Step 1: Set up the proportion
Let the height of the tree be meters. The pole's height is 33 meters, and the pole's shadow is 44 meters long. The tree's shadow is 1515 meters long.
We can set up the proportion as follows:
Substitute the known values:
Step 2: Solve for
Cross-multiply to solve for :
Now, divide both sides by 44 to find :
Thus, the height of the tree is approximately 1136.75 meters.
However, there seems to be an error. I have incorrectly made the numbers seem unreasonable. Let me clarify
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Math Problem Analysis
Mathematical Concepts
Similar Triangles
Proportions
Formulas
Proportion formula: height of pole / length of pole's shadow = height of tree / length of tree's shadow
Theorems
Similar triangles theorem
Suitable Grade Level
Grades 7-9