solve each triangle using either the Law of Sines or the Law

solve each triangle using either the Law of Sines or the Law of Cosines. If no triangle exists, write “no solution.” Round your answers to the nearest tenth.

1. A = 23°, B = 55°, b = 9

2. A = 18°, a = 25, b = 18

Solution

1) A = 23⁰ , B = 55⁰ , b = 9

C = 180 - A - B

C = 180 - 23 - 55 = 102

from sine formula :

sin A / a = sin B / b = sin C / c

from sin A / a = sin B / b

sin 23 / a = sin 55 / 9

a = sin 23 * 9 / sin 55

a = 4.29

from sin B / b = sin C / c

sin 55 / 9 = sin 102 / c

c = sin 102 *9 / sin 55

c = 10.746

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2) A = 18⁰ , a = 25, b = 18

from sine formula:

sin A / a = sin B / b = sin C / c

from sin A / a = sin B / b

sin 18 / 25 = sin B / 18

sin B = 0.2224

B = sin^-1 ( 0.2224)

B = 12.85 degree

C = 180 - A- B

= 180 - 18 - 12.85 = 149.15

from sin B / b = sin C / c

sin (12.85) / 18 = sin ( 149.15) / c

c = 41.50