In his 1678 " Trait?de la Lumi�re ", Christiaan Huygens showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the Huygens Fresnel principle.
22.
Neumann s triangle is consistent with the geometrical restriction that \ alpha + \ beta + \ theta = 2 \ pi, and applying the law of sines and law of cosines to it produce relations that describe how the interfacial angles depend on the ratios of surface energies.
23.
According to Glen Van Brummelen, " The Law of Sines is really Regiomontanus's foundation for his solutions of right-angled triangles in Book IV, and these solutions are in turn the bases for his solutions of general triangles . " Regiomontanus was a 15th-century German mathematician.
24.
The law of tangents, although not as commonly known as the law of sines or the law of cosines, is equivalent to the law of sines, and can be used in any case where two sides and the included angle, or two angles and a side, are known.
25.
The law of tangents, although not as commonly known as the law of sines or the law of cosines, is equivalent to the law of sines, and can be used in any case where two sides and the included angle, or two angles and a side, are known.
26.
He listed the six distinct cases of a right-angled triangle in spherical trigonometry, and in his " On the Sector Figure ", he stated the law of sines for plane and spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for both these laws.
27.
:The significance of the law of sines and the law of cosines is that you can use them to solve a triangle if you know two sides and an angle ( law of cosines ) or two angles and a side ( law of sines ) . & # x2013; b _ jonas 12 : 13, 28 March 2006 ( UTC)
28.
:The significance of the law of sines and the law of cosines is that you can use them to solve a triangle if you know two sides and an angle ( law of cosines ) or two angles and a side ( law of sines ) . & # x2013; b _ jonas 12 : 13, 28 March 2006 ( UTC)
29.
Applying the law of sines and the fact that triangle angles sum to ? radians, we get that the angle that the half shadow subtends at the center of the farther sphere is \ theta = \ pi-\ arcsin \ frac rx-\ arcsin \ frac { rX } { Rx }, where capital letters apply to the farther sphere.
30.
Just as three quantities whose equality is expressed by the law of sines are equal to the diameter of the circumscribed circle of the triangle ( or to its reciprocal, depending on how the law is expressed ), so also the law of cotangents relates the radius of the inscribed circle of a triangle ( the inradius ) to its sides and angles.
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