Aclimber is standing at the top of mount kilimanjaro, approximately 3.7 miles above sea level. the radius of the earth is 3959 miles. what is the climber's distance to the horizon?

For the answer to the question above,The tangent line from the horizon to the radius of the earth is perpendicular between the tangent point and the center. So, therefore, we can use Pythagorean's theorem to write an equation:

x² + r² = (r+h)²
x² + 3959² = (3959 + 3.7)²
x² = 3962.7² - 3959²
x = 171.2 miles
I hope this helps