Question

A climber is standing at the top of Mount Kazbek, approximately 3.1 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?

Answer 1

I just took a test for K12 with this question. Your answer will be 156.7 miles 

Answer 2

The radius of the earth = OC = OB = 3959 miles

Peak of the Mount Kazbek = A = 3.1 miles

OA = OC + CA

OA = 3959 + 3.1 = 3962.1 miles

As OBA is a right triangle,

`OA^(2)` =
`OB^(2)` +
`AB^(2)`

`3962.1^(2)` =
`3959^(2)` +
`AB^(2)`

15698236.41 = 15673681 +
`AB^(2)`

`AB^(2)` = 15698236.41 - 15673681

`AB^(2)` =24555.41

AB = 156.701659

climber's distance to the horizon is 156.7 miles