EXAMPLE 1

1. Solve ABCwith C = 107°,B = 25°, and b = 15. = = a a 15 15 15 c c sin 48° sin 48° sin 25° sin 25° sin 25° sin 107° sin 107° Write two equations, each = = with one variable. EXAMPLE 1 Solve a triangle for the AAS or ASA case SOLUTION First find the angle:A = 180° – 107° – 25° = 48°. By the law of sines, you can write

2. 15 sin 107° a = c = sin 25° a c 26.4 33.9 InABC,A = 48°,a 26.4,andc 33.9. ANSWER 15 sin 48° sin 25° EXAMPLE 1 Solve a triangle for the AAS or ASA case Solve for each variable. Use a calculator.

3. Solve ABC. First find the angle: A = 180° – 34° – 100° = 46°. 8 = = sin 34° a a 8 8 c c sin 46° sin 46° sin 34° sin 34° sin 100° sin 100° Write two equations, each = = with one variable. for Example 1 GUIDED PRACTICE 1. B = 34°,C = 100°,b = 8 SOLUTION By the law of sines, you can write

4. 8 sin 100° a = c = sin 34° a c 14.1 10.3 ANSWER InABC,A 46°,a 10.3,andc 14.1. 8 sin 46° sin 34° for Example 1 GUIDED PRACTICE Solve for each variable. Use a calculator.

5. Solve ABC. First find the angle: C = 180° – 51° – 44° = 85°. b 11 = = sin 44° sin 85° a a 11 11 b sin 51° sin 51° sin 85° sin 85° Write two equations, each = = sin 44° with one variable. for Example 1 GUIDED PRACTICE 2. A = 51°, B = 44°,c = 11 SOLUTION By the law of sines, you can write

6. 11 sin 51° 11 sin 44° a = b = sin 85° sin 85° b a 8.6 7.7 ANSWER InABC,A 85°,a 8.6,andb 7.7. for Example 1 GUIDED PRACTICE Solve for each variable. Use a calculator.