Final answer:
To find the car's distance from a point directly below the helicopter, we use the tangent of the angle of elevation (90 degrees minus the angle of depression) and the helicopter's altitude, resulting in approximately 346 feet.
Step-by-step explanation:
The student asked about determining the distance of a car from a point directly below a helicopter, given an angle of depression and the helicopter's altitude. To solve this, we apply trigonometry, specifically the tangent function which uses the opposite side (the car's distance from the point below the helicopter) and the adjacent side (the helicopter's altitude). The angle of depression is the angle between the horizontal line from the helicopter and the line of sight to the car. Since the angles of depression and elevation are complementary to the angle from the horizontal plane, we can use the elevation angle (which is 90° minus the angle of depression) in our calculations:
- Angle of elevation = 90° - 77° = 13°
- Tangent of the angle of elevation (tan 13°) = opposite side / adjacent side (car's distance / 1500 ft)
- Using a calculator to find tan 13°, and then rearrange the formula to solve for the car's distance:
- Car's distance = 1500 ft * tan 13°
- Car's distance ≈ 1500 ft * 0.2309
- Car's distance ≈ 346.35 ft
To the nearest foot, the car is approximately 346 feet from the point directly below the helicopter.