Earth's Circumference
Baghdad, IraqAround CE 830, Caliph Al-Ma'mun commissioned a group of Muslim astronomers led by Al-Khwarizmi to measure the distance from Tadmur (Palmyra) to Raqqa, in modern Syria. They calculated the Earth's circumference to be within 15% of the modern value, and possibly much closer. How accurate it actually was is not known because of uncertainty in the conversion between the medieval Arabic units and modern units, but in any case, technical limitations of the methods and tools would not permit an accuracy better than about 5%.
A more convenient way to estimate was provided in Al-Biruni's Codex Masudicus (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two different locations, al-Biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which made it possible for it to be measured by a single person from a single location. From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he calculated beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines. However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted the value calculated the previous century by the al-Ma'mun expedition.