Earth's radius is about 4000 mi. To the nearest mile, what is the distance a person can see on a clear day from an airplane 5 mi above the Earth?
200 mi
63 mi
4000 mi
5660 mi

Draw a diagram. You want to see how far the horizon is from height h. Draw a radius extended by h. Draw the tangent to the circle from that extended radius. Draw a radius to the tangent. Now you have a right triangle with one leg=r, the hypotenuse=r+h.

If the distance to the horizon is d, then

r^2 + d^2 = (r+h)^2

4000^2 + d^2 = 4005^2

d^2 = 16040025 - 16000000 = 40025

d = 200 mi.

If r is very large compared to h, then we have

(r+h)^2 = r^2 + 2rh + h^2

but h^2 is negligible.

so, d^2 = 2rh = 2*4000*5 = 40000

d = 200

stethere all not eveanp-by-step explanation: