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 A₁ is smaller than A₂.)

b = 42,    c = 41,    C = 35°

A₁ =

A₂ =

B₁ =

B₂ =

a₁ =

a₂ =

Solution

b = 42

c = 41

angle C = 35

applying law of sines

c / sin C = b / sin B

41 / sin 35 = 42 / sin B

sin B = 42 / 71 .48

B1 = 35.98 deg ; B2 = 180 -35.98 = 144.01 deg

A1 = 180 - 35.98 - 35 = 109.05 deg ; A2 = 180 - 144.01 - 35 = 1.0 deg

a1/sinA1 = c/sinC ----> a1 = sin109.05*41/sin35 = 67.6

a2/sinA2 = c/sinc -----> a2 = sin1*41/sin35 = 1.25 = 1.3