Math 41 Section 9.2 - 9.2 The Law of Sines If none of the...

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9.2 The Law of Sines - If none of the angles in a triangle are a right angle, the triangle is called oblique . An oblique triangle will have either three acute angles or two acute angles and one obtuse angle. Solving Oblique Triangles Need to know: Case 1: One side and two angles (ASA or SAA) Case 2: Two sides and the angle opposite of one of them are known (SSA) Case 3: Two sides and the included angle are known (SAS) Case 4: Three sides are known (SSS) Law of Sines For a triangle with sides a, b, c and opposite angles A, B, C, respectively, sinAa = = sinBb sinCc A + B + C = 180 o Example 1: Using the Law of Sines to Solve a SAA Triangle Solve the triangle: A = 40 o , B = 60 o , a = 4 Solution: The third angle is found using A + B + C = 180 A + B + C = 180 40 + 60 + C = 180 C = 80 Now we use the law of sines twice to find the unknown sides b and c. ((sin 40) / 4) = ((sin 60) / b) ((sin 40) / 4) = ((sin 80) / c) b = ((4 sin 60) / sin 40) = 5.39 c = ((4 sin 80) / sin 40) = 6.13 - SSA, which applies to triangles for which two sides and the angle opposite one of them are known, is referred to as the
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