Use the Law of Sines to solve for all possible triangles tha

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that B_1 is smaller than B_2.) a = 39, c = 42, A = 38 degree

Solution

a = 39 , c = 42 , A = 38

applying law of sines

a / sin A = c / sin C

39 / sin 38 = 42 / sin C

sin C = 42 / 63.3465

C1 = 41.5 degrees

C2 = 138.5

B2 = 180 - ( 41.5 + 38 )

B2 = 100.5

B1 = 3.5

39/ sin 38 = b1 / sin 3.5

b1 = 3.9

b2 = 62.3