pilot in a helicopter spots a landing pad belou. If the angle of depression is 73 and the horizont stance to the pad is 1200 feet, what is the altitude of the helicopter?

To determine the altitude of the helicopter, we can use trigonometry, specifically the tangent function, which relates the angle of depression to the altitude and horizontal distance. **Given:** - Angle of depression (\( \theta \)) = 73° - Horizontal distance (\( d \)) = 1200 feet **Step-by-Step Solution:** 1. **Understand the Right Triangle:** - The angle of depression (\( \theta \)) is the angle between the horizontal line from the pilot's eye and the line of sight to the landing pad. - This forms a right triangle where: - The **adjacent side** is the horizontal distance (\( d = 1200 \) feet). - The **opposite side** is the altitude (\( h \)) of the helicopter, which we need to find. 2. **Use the Tangent Function:** \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \] \[ \tan(73°) = \frac{h}{1200} \] 3. **Solve for Altitude (\( h \)):** \[ h = 1200 \times \tan(73°) \] 4. **Calculate \( \tan(73°) \):** \[ \tan(73°) \approx 3.271 \] 5. **Compute the Altitude:** \[ h = 1200 \times 3.271 \approx 3925 \text{ feet} \] **Conclusion:** The altitude of the helicopter is approximately **3,925 feet**.