pre-calc 6.1&6.2 - Section 6.1 The Law of Sines The...

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The Law of Sines The Law of Sines and Its Derivation An oblique triangle is a triangle that does not contain a right angle. An oblique triangle has either three acute angles or two acute angles and one obtuse angle. The angles are labeled A, B, and C. The sides opposite each angle are labeled as a, b , and c , respectively. The Law of Sines If A, B, and C are the measures of the angles of a triangle, and a, b , and c are the lengths of the sides opposite these angles, then C c B b A a sin sin sin = = . The ratio of the length of the side of any triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Solving Oblique Triangles Solving an oblique triangle means finding the lengths of its sides and the measurements of its angles. The Law of Sines can be used to solve a triangle in which one side and two angles are known. The known measurements can be abbreviated using SAA (a side and two angles are known) or ASA (two angles and the side between them are known). EX 1: Solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.
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pre-calc 6.1&6.2 - Section 6.1 The Law of Sines The...

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