Law of Sines and Cosines Essay Example

Law of Sines and Cosines Paper Law of sines In  trigonometry, the  law of sines  (also known as the  sine law,  sine formula, or  sine rule) is anequation  relating the  lengths  of the sides of an arbitrary  triangle  to the  sines  of its angles. According to the law, where  a,  b, and  c  are the lengths of the sides of a triangle, and  A,  B, and  C  are the opposite angles (see the figure to the right). Sometimes the law is stated using the  reciprocal  of this equation: 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. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an  ambiguous case. The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, the other being the  law of cosines. Law of cosines In  trigonometry, the  law of cosines  (also known as the  cosine formula  or  cosine rule) is a statement about a general  triangle  that relates the lengths of its sides to the  cosine  of one of itsangles. We will write a custom essay sample on Law of Sines and Cosines specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Law of Sines and Cosines specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Law of Sines and Cosines specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Using notation as in Fig. 1, the law of cosines states that where ? denotes the angle contained between sides of lengths  a  and  b  and opposite the side of lengthc. The law of cosines generalizes the  Pythagorean theorem, which holds only for  right triangles: if the angle  ? s a right angle (of measure 90 °Ã‚  or ? /2 radians), then cos(? ) = 0, and thus the law of cosines reduces to The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known. By changing which legs of the triangle play the roles of  a,  b, and  c  in the original formula, one discovers that the following two formulas also state the law of cosines: