The plane law of sines was later described in the 13th century by Nas + r al-D + n al-Tks + .
12.
He also stated the law of sines for spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for these laws.
13.
The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known a technique known as triangulation.
14.
In his " On the Sector Figure ", he stated the law of sines for plane and spherical triangles, and provided proofs for this law.
15.
Unfortunately, Medieval sailors with the rudimentary educational levels of the 14th and 15th centuries, were not likely to know the Law of Sines or manipulate it with ease.
16.
Ibn Mu?dh al-Jayyn + 's " The book of unknown arcs of a sphere " in the 11th century introduced the general law of sines.
17.
By substituting 0 } }, 1 } }, and " 1 } }, one obtains respectively the Euclidean, spherical, and hyperbolic cases of the law of sines described above.
18.
However, it does not tackle the traverse problem in one go, like the Law of Sines, but rather splits the problem into two right-angled triangles which it proceeds to solve successively.
19.
Ibn Mu?dh al-Jayyn + is one of several Islamic mathematicians to whom the law of sines is attributed; he wrote his " The Book of Unknown Arcs of a Sphere " in the 11th century.
20.
The spherical law of sines was discovered in the 10th century : it has been attributed variously to Abu-Mahmud Khojandi, Nasir al-Din al-Tusi and Abu Nasr Mansur, with Abu al-Wafa'Buzjani as a contributor.
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