Height of a Tree Using Trigonometry

Consider the following scenario involving a right triangle where the angle of elevation from the horizontal to the top of a tree is $$30^\circ$$. If the distance from the observer to the base of the tree is 50 feet, how tall is the tree, rounded to the nearest foot?

To solve this problem, you can use trigonometric ratios, particularly the tangent function, which is defined as the ratio of the opposite side to the adjacent side. Recall that for a right triangle:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

In this case, the side opposite the angle is the height of the tree (let's denote it as $$h$$), and the adjacent side is the distance from the observer to the base of the tree (50 feet). Set up the equation based on the given information.