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Answer:
[tex]\color{green}{\displaystyle \rule{200pt}{1pt}} \\\tiny{\begin{gathered}\textsf{Given problem:} \\\text{A tree casts a shadow that is 57 feet long and the angle from the tip of the shadow to the top of the tree is 27˚.} \\\text{Find the height of the tree.} \\\textsf{Step 1: Understand the trigonometric relationship.} \\\text{The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.} \\\tan(\text{angle}) = \frac{\text{opposite side}}{\text{adjacent side}} \\\textsf{Step 2: Use the tangent function to find the height of the tree.} \\\tan(27^\circ) = \frac{\text{height of tree}}{57} \\\text{Given that } \tan(27^\circ) \approx 0.5095, \text{ we can solve for the height of the tree:} \\\text{height of tree} = 57 \times \tan(27^\circ) \\\text{height of tree} = 57 \times 0.5095 \\\text{height of tree} \approx 29.04 \text{ feet} \\\textsf{Therefore, the height of the tree is approximately } 29.04 \text{ feet.} \\\color{green}{\displaystyle \rule{200pt}{1pt}}\end{gathered}}[/tex]
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