2. A helicopter that is 700 feet in the air measures the angle of depression to a landing pad as \( 24^{\circ} \). How far is the landing pad from the point directly beneath the helicopter's current position?

To solve this problem, we can use some trigonometry! The angle of depression is the angle formed between the horizontal line from the helicopter and the line of sight down to the landing pad. Since the helicopter is 700 feet high, we can create a right triangle where the height represents the opposite side (700 feet) and the distance to the landing pad is the adjacent side. Using the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \\ \text{Let } D = \text{distance to the landing pad} \\ \tan(24^{\circ}) = \frac{700}{D} \] Rearranging gives us: \[ D = \frac{700}{\tan(24^{\circ})} \] Calculating this yields: \[ D \approx \frac{700}{0.4452} \approx 1570.81 \text{ feet} \] So, the landing pad is approximately 1570.81 feet from the point directly below the helicopter! To visualize this, imagine dropping a straight line down from the helicopter to the ground; that point marks where you'd find the landing pad if you walked directly toward it at a slant. It's like using your compass skills but with a bit of math to find just how far you'll be strolling!