The angle relative to the horizontal from the top of a tree to a point 14 feet from its base (on flat ground) is \( 30^{\circ} \). Find the height of the tree. The height of the tree is approximately \( \square \) feet. (Round to one decimal place as needed.)

To determine the height of the tree, let's analyze the situation step by step. ### Given: - **Distance from the base of the tree to the point on the ground:** 14 feet - **Angle of depression from the top of the tree to the point:** \( 30^{\circ} \) ### Visualization: Imagine a right triangle where: - The **horizontal leg** (adjacent side) is 14 feet. - The **vertical leg** (opposite side) is the height of the tree, which we need to find. - The **angle** between the horizontal leg and the hypotenuse (line of sight) is \( 30^{\circ} \). ### Using Trigonometry: The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] Here, \(\theta = 30^{\circ}\), the Opposite side is the height \( h \), and the Adjacent side is 14 feet. \[ \tan(30^{\circ}) = \frac{h}{14} \] \[ h = 14 \times \tan(30^{\circ}) \] \[ \tan(30^{\circ}) = \frac{1}{\sqrt{3}} \approx 0.5774 \] \[ h \approx 14 \times 0.5774 \approx 8.082 \text{ feet} \] ### Conclusion: Rounding to one decimal place, the height of the tree is approximately **8.1 feet**. \[ \boxed{8.1} \]