Pre-Calc Exam Notes 43

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

Ask a homework question - tutors are online