A climber is standing at the top of a mountain, approximately 2.5 mi above sea level. The radius of the Earth is 3959 mi. What is the climber's distance to the horizon?

round final answer to the nearest tenth

Given:

The climber is at 2.5 miles above sea level

The Earth's radius is 3959 miles

We need to determine the climber's distance to the horizon.

let R = radius of the Earth

D = distance to the horizon

Use the Pythagorean Theorem to solve for the distance of the climber to the horizon. The two legs of the right triangle are the radius of the Earth and the distance of the climber to the horizon.

R^2 + D^2 = (R + 2.5) ^2

3959^2 + D^2 = (3959 + 2.5) ^2

solve for D:

D = 208.68 miles

Therefore, the climber is 208.68 miles from the horizon.