Question

The summit of Mount Mauna Kea is approximately 13,796 ft above sea level. What is the distance from the summit to the horizon, rounded to the nearest mile

Answer 1

About 145 miles.

Step-by-step explanation:

Assume that the distance from the center of the earth to any point on the earth's surface is 4,000 miles.

Step-by-step explanation:

r = 4000

v = 13796/5280

(divide by 5280 to convert to miles)

Using Pythagorean's Theorem:

a^2 + b^2 = c^2

a^2 + 4000^2 = (4000 + 13796 /5280)^2

a^2 = (4000 + 13796 /5280)^2 − 4000^2

a = √(4000 + 13796 /5280)^2 − 4000^2 ≈ 144.6

This is just a shrunk down version so it is easier to read. All credit goes to the other answer.

Answer 2

About 145 miles.

Explanation:

Assume that the distance from the center of the earth to any point on the earth's surface is 4,000 miles.

Step-by-step explanation:

r

=

4000

v

=

13796

5280

(divide by 5280 to convert to miles)

Using Pythagorean's Theorem:

a

2

+

b

2

=

c

2

a

2

+

4000

2

=

(

4000

+

13796

5280

)

2

a

2

=

(

4000

+

13796

5280

)

2

−

4000

2

a

=

√

(

4000

+

13796

5280

)

2

−

4000

2

≈

144.6