Help? 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.
Draw a diagram. There is a right angle at the horizon, so the distance d is
4000^2 + d^2 = (4000 + 29035/5280)^2
you can compare that to the estimate of
d = √(2Rh)
To calculate the distance from the summit of Mount Everest to the horizon, we can use a simple formula:
d = √(2Rh),
where:
- d is the distance from the summit to the horizon,
- R is the radius of the Earth (4,000 miles in this case),
- h is the height above the surface (29,035 ft).
First, let's convert the height to miles:
29,035 ft ÷ 5,280 ft/mile = 5.5 miles (rounded).
Now we can calculate the distance:
d = √(2 * 4,000 miles * 5.5 miles)
d ≈ √(44,000 miles^2)
d ≈ 209.76 miles
Therefore, the distance from the summit of Mount Everest to the horizon, rounded to the nearest mile, is approximately 210 miles.
To calculate the distance from the summit of Mount Everest to the horizon, we can use the Pythagorean theorem. The distance from the Earth's center to any point on Earth's surface is given as 4,000 miles.
Let's define "d" as the distance from the summit of Mount Everest to the horizon.
To use the Pythagorean theorem, we need to break down the distance into two components: the vertical component (h) and the horizontal component (r).
The vertical component (h) is the height of Mount Everest above sea level, which is 29,035 ft. To convert this to miles, we divide by 5,280 (the number of feet in a mile):
h = 29,035 ft / 5,280 ft/mile ≈ 5.49 miles
The horizontal component (r) is the distance from the Earth's center to the summit of Mount Everest. We subtract the radius of the Earth (4,000 miles) from the distance of the summit above sea level:
r = 4,000 miles + 5.49 miles ≈ 4005.49 miles
Now we can use the Pythagorean theorem to find d:
d^2 = h^2 + r^2
d^2 = 5.49^2 + 4005.49^2
d ≈ √(5.49^2 + 4005.49^2)
d ≈ 4005.49 miles
Therefore, the distance from the summit of Mount Everest to the horizon, rounded to the nearest mile, is approximately 4005 miles.