What is the Distance to the Moon?

Using the calculations on the diameter of the Earth, the Greeks reasoned that the larger triangle would measure one Earth diameter at its base (12,875 km/8000 miles) and be 1,390,000 km (864,000 miles) long. The other triangle would be the equivalent of 2.5 Moon diameters wide and, since the triangles are proportionate, 2.5 Moon orbits tall.

Adding the two triangles together would yield the equivalent of 3.5 Moon orbits, which would create the largest triangle and gave the (again, relatively) accurate measurement of the distance between the Earth and the Moon. In other words, the distance is 1.39 million km (864,000 miles) divided by 3.5, which works out to around 397,500 km (247,000 miles). Not exactly bang on, but not bad for ancient peoples!