Math Problem Statement
From some distance away, you measure the angle of elevation to the top of a tree to be 30 degrees. Walking 20 feet closer, you measure the angle of elevation to be 45 degrees. How tall is the tree? No decimal answers, solution is exact.
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Angle of Elevation
Tangent Function
System of Equations
Formulas
tan(θ) = opposite / adjacent
h = d / √3
h = d - 20
Difference of squares: (a - b)(a + b) = a^2 - b^2
Theorems
Trigonometric identity for tangent
Rationalization of the denominator
Suitable Grade Level
Grades 9-12
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