Around 270 BC, a Greek worked out how far away the Sun is using nothing but a half moon and an angle.

When the Moon is exactly half lit, the Sun, Moon and Earth form a right angle at the Moon, so measuring the Moon-to-Sun angle in your sky gives you the ratio of the two distances by simple trigonometry. Aristarchus measured 87° and concluded the Sun was about 20 times farther away. The real angle is 89.85° and the real answer is about 390. His method was perfect; his protractor wasn't.