Question

Geo help please; Denali peaks at 20,320 ft. What is the distance from this peak to the horizon, rounded to the nearest mile? Assume that the distance from the center of the earth to any point on the earth's surface is 4,000 miles.
Answer choices:
≈ 166 mi
≈ 176 mi
≈ 173 mi
≈ 148 mi

Answer 1

We have a triangle.

The horizon is the surface of the earth as seen from the top of the mountain. (line b). We know the radius of the earth (line a). We need to calculate line c.

We have a right triangle with the 90 degree angle being where line a and b intersect at the surface of the earth.

This will make use of Pythagorean's theorem.

But first, we need to convert 20,320 ft into miles so that the units of the equation are all the same.

There are are 5820 feet in each mile. To get the height of the mountain in miles, you'll need to divide the height by 5820. We will add this value to the radius of the earth to get the distance of line c.

Then we plug all this into our equation. \[4000^2 + b^2 = \left ((4000)+{\left (20320 \over 5820 \right )} \right)^2\]

You can solve for b, which will be the distance from the top of the mountain to the horizon.

Answer 2

So confused. Doesn't help at all.

Answer 3

Would've fanned and given a medal if this would've helped me.