PP Section 9.2 - The Law of Sines and The Law of Cosines...

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The Law of Sines and The Law of Cosines
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Objective To learn to solve triangles that are NOT right triangles. If none of the angles of a triangle is a right angle, the triangle is called oblique. To solve an oblique triangle means to find the lengths of its sides and the measurements of its angles.
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All angles are acute Two acute angles, one obtuse angle There are two types of oblique triangles.
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CASES FOR SOLVING AN OBLIQUE TRIANGLE CASE 1: One side and two angles are known (SAA or ASA). CASE 2: Two sides and the angle opposite one of them are known (SSA). CASE 3: Two sides and the included angle are known (SAS). CASE 4: Three sides are known (SSS).
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The Law of Sines is used to solve SAA, ASA or SSA triangles, which are cases 1 and 2. Law of Sines For a triangle with sides and opposite angles , , , respectively, a b c , , αβγ sin sin sin α β γ a b c = =
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=30 (SAA) α β o o , , = = 70 5 a 70 o 30 o 5 b c γ + + = 180 o 30 70 180 o o o + + = = o o c
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PP Section 9.2 - The Law of Sines and The Law of Cosines...

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