A drone is flying at a height of 100 feet above ground level. If the angle of depression from the drone to a point on the ground is 45 degrees, what is the horizontal distance of that point from the drone's position?

To determine the horizontal distance from the drone to the point on the ground, we can use trigonometry, specifically the tangent function, which relates the angle of depression to the opposite and adjacent sides of a right triangle. Here's a step-by-step breakdown: 1. **Identify the Given Values:** - **Height (opposite side)**: 100 feet - **Angle of depression**: 45 degrees 2. **Understand the Triangle:** - The angle of depression from the drone to the point on the ground creates a right triangle where: - The **opposite side** is the height of the drone above ground: 100 feet. - The **adjacent side** is the horizontal distance we need to find. - The **angle** between the horizontal line (adjacent side) and the line of sight (hypotenuse) is 45 degrees. 3. **Use the Tangent Function:** \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Plugging in the known values: \[ \tan(45^\circ) = \frac{100 \text{ feet}}{x} \] Since \(\tan(45^\circ) = 1\): \[ 1 = \frac{100}{x} \implies x = 100 \text{ feet} \] **Conclusion:** The horizontal distance from the drone to the point on the ground is **100 feet**. **Answer:** 100 feet