Using the tangent function with the given angle of elevation (66°) and adjacent side (68 feet), the height of the tree is approximately 153.5 feet.
1. The problem involves a right triangle with a known angle of elevation (66°) and a known adjacent side (68 feet).
2. We need to find the opposite side, which is the height of the tree.
3. We can use the tangent function, which relates the opposite side and the adjacent side of a right triangle to an angle.
4. The formula is: tan(theta) = opposite/adjacent
5. Plug in the given values and solve for the opposite side:
tan(66°) = opposite/68
opposite = 68 * tan(66°)
opposite ≈ 153.5 feet
Therefore, the height of the tree is approximately 153.5 feet.