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ss_7_2

# ss_7_2 - Section 7.2 The Law of Sines In this section we...

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Section 7.2 The Law of Sines In this section, we discuss solving triangles, and we use the law of sines to solve some triangles. An obtuse angle is an angle between 90 o and 180 o . An oblique triangle is a triangle that does not contain a 90 o angle. Labeling triangles: a , b , c will be the sides opposite the angles α , β , γ , respectively. A , B , C will be the vertices of angles α , β , γ , respectively. The Law of Sines The following relationships hold for any triangle. Law of Sines: sin α a = sin β b = sin γ c . Solving Triangles: In the following, S stands for side and A stands for angle, and SAA means side-angle-angle, in that order. Case 1 : SAA or ASA (use Law of Sines) Case 2 : SSA (use Law of Sines) Case 3 : SAS (use Law of Cosines) Case 4 : SSS (use Law of Cosines) The following triangles illustrate the above cases. We now consider triangles that can be solved with the Law of Sines. Case 1: SAA Example. Solve the triangle if α = 50 o , β = 25 o , a = 4. Solution. Since α = 50 o and β = 25 o , γ = 180 o - (25 o + 50 o ) = 105 o . By the law of sines, sin α a = sin β b = sin γ c . Hence, sin 50 o 4 = sin 25 o b = sin 105 o c . Thus, b = 4 sin 25 o sin 50 o = 2 . 2 c = 4 sin 105 o sin 50 o = 5 . 0

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ss_7_2 - Section 7.2 The Law of Sines In this section we...

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