Question

1. how tall is the tree?

tan(\theta) = \frac{20}{50}
options: 50 feet, 30 feet, 70 feet, 20 feet

Explanation:

Step1: Analyze the tangent formula

We know that \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). In the context of the tree, the height of the tree (let's call it \(h\)) and the distance from the person to the tree (50 feet) form a right triangle, where \(\tan(\theta)=\frac{h}{50}\) (wait, but the given \(\tan(\theta)=\frac{20}{50}\)? Wait, maybe there's a misinterpretation. Wait, no—wait, maybe the 20 is a typo? Wait, no, looking at the options, the correct approach: Wait, actually, maybe the formula is \(\tan(\theta)=\frac{\text{height}}{50}\), but the given \(\tan(\theta)=\frac{20}{50}\) is incorrect? Wait, no, maybe the height is 20? Wait, no, the options include 20 feet. Wait, let's re - examine.

Wait, the formula given is \(\tan(\theta)=\frac{20}{50}\). But in a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). If the adjacent side (distance) is 50, and the opposite side is the height of the tree. So if \(\tan(\theta)=\frac{20}{50}\), that would mean the height (opposite) is 20, and adjacent is 50. So the height of the tree is 20 feet.

Step2: Match with options

Looking at the options: 50 feet, 30 feet, 70 feet, 20 feet. The value that matches the height from the tangent formula (where \(\tan(\theta)=\frac{20}{50}\), so opposite side (height) is 20) is 20 feet.

Answer:

20 feet (the option with "20 feet")