Please help with geometry homework

Question

When railroads were first laid across the flat midwestern prairie, the train engeneers reported that they could see for miles from their cabs 12 feet above the ground. Were they exaggerating? If not how many miles could they see? (5280 ft= 1 mile, 3960 miles- earths radius)

Answer 1

The hypotenuse is 3960*5280+12.= H

The long leg is 3960*5280 = L

The sight distance is sqrt(H² - L²) which according to my calculation would be a little more than 4 miles.