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Pre-Calc Exam Notes 43

# Pre-Calc Exam Notes 43 - The Law of Sines Section 2.1 43 If...

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The Law of Sines Section 2.1 43 If C is obtuse, then 180 C is acute, as are A and B . If A > 180 C then A + C > 180 , which is impossible. Thus, we must have A 180 C . Likewise, B 180 C . So by what we showed above for acute angles, we know that sin A sin (180 C ) and sin B sin (180 C ). But we know from Section 1.5 that sin C = sin (180 C ). Hence, sin A sin C and sin B sin C when C is obtuse. Thus, sin A sin C if C is acute or obtuse, so by the Law of Sines we have a c = sin A sin C sin C sin C = 1 a c 1 a c . By a similar argument, b c . Thus, a c and b c , i.e. c is the largest side. QED Exercises For Exercises 1-9, solve the triangle ABC . 1. a = 10, A = 35 , B = 25 2. b = 40, B = 75 , c = 35 3. A = 40 , B = 45 , c = 15 4. a = 5, A = 42 , b = 7 5. a = 40, A = 25 , c = 30 6. a = 5, A = 47 , b = 9 7. a = 12, A = 94 , b = 15 8. a = 15, A = 94 , b = 12 9. a = 22, A = 50 , c = 27 10. Draw a circle with a radius of 2 inches and inscribe a triangle inside the circle. Use a ruler and
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