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LAW OF SINES The law of sines provides a direct approach to the solution of oblique triangles, avoiding the necessity of subdividing into right triangles. Let the triangle in figure 1921 (A) represent any oblique triangle with all of its angles acute. The labels used in figure 1921 are standardized. The small letter a is used for the side opposite angle A; small b is opposite angle B; small c is opposite angle C. Figure 1920.(A) Oblique triangle with all angles acute; (B) obtuse triangle. Figure 1921.(A) Acute oblique triangle with standard labels; (B) obtuse triangle with standard labels. The law of sines states that in any triangle, whether it is acute as in figure 1921 (A) or obtuse as in figure 1921 (B), the following is true: EXAMPLE: In figure 1921 (A), let angle Abe 15° and let angle C be 85°. If BC is 20 units, find the length of AB. SOLUTION: By the law of sines,

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