Question

Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water’s edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Left Figure, where h = 1.5 m, estimate the radius R of the Earth.

Answer 1

The question can be tackled by simply using Pythagoras' theorem.

The length of the hypotenuse is = (R + h) meters = R + 1.5 meters

height (or base) = R meters

d = 4400 meters

therefore by Pythagoras' theorem,

(R + 1.5)² = R² + 4400²

R² + 3R + 2.25 = R² + 119360000

therefore R = 6453332.58 m or 6453.33 km