The summit of Mount Everest is approximately 29,035 ft above sea level. What is the distance from the summit to the horizon, rounded to the nearest mile? Assume that the distance from the Earth's center to any point on Earth's surface is 4,000 miles. How do I solve this?
To find the distance from the summit of Mount Everest to the horizon, you can use the concept of the Earth's curvature. Here's how you can solve it:
1. Determine the radius of the Earth: Given that the distance from the Earth's center to any point on its surface is 4,000 miles, the radius of the Earth can be calculated by dividing this distance by 2π (since the radius is half the circumference of a circle).
Radius = 4,000 miles / (2 * π) = 4,000 / 6.28 ≈ 637.1 miles
2. Calculate the distance from the summit of Mount Everest to the horizon: To calculate this distance, you need to consider two lengths: the radius of the Earth and the height of Mount Everest.
Distance = √((Radius + Height)^2 - Radius^2)
Distance = √((637.1 + 29,035)^2 - 637.1^2)
3. Use a calculator or a mathematical software to compute the expression.
Distance ≈ √((29,672)^2 - 405,017)
Distance ≈ √(879,928,384 - 405,017)
Distance ≈ √879,523,367
Distance ≈ 29,644 miles (rounded to the nearest mile)
Therefore, the distance from the summit of Mount Everest to the horizon is approximately 29,644 miles.