Law of Sines. Need help solving problem

Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. There may be two triangles, one triangle, or no triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Enter all angles in degrees. Round your answers to one decimal place. Below, enter your answers so that ∠A₁ is smaller than ∠A₂.)

b = 22,   c = 31,   ∠B = 29°

∠A₁

    ∠A₂

∠C₁

 ∠C₂

a₁

a₂

Answer 1

b = 22 c = 31 B =29

what are the other sides and angles of the triangle?? a=11, A=14.09, C=136.91

or a= 43.18, A=107.91, C= 43.09

use law of sines

sinC/31 = sin29/22

C = arcsin(sin29(31/22)= about 43.09 degrees or 180-43.09=136.91

A = 180-C - 29= 151-43.09= 107.91 or 180-136.91-29= 14.09

a/sinA = 22/sin29

a = 22sinA/sin29

= about 43.18 or 11

Answer 2

sinC/31 = sin29°/22

22sinC = 31sin29°

sinC = 0.6831408

∠C = Sin^-1(0.6831408) or 180° - Sin^-1(0.6831408) = 43.1° or 136.9°

If ∠C = 43.1°, then ∠A = 180° - 29° - 43.1° = 107.9°

If ∠C = 136.9°, then ∠A = 180° - 29° - 136.9° = 14.1°

There are 2 triangles:

First triangle: ∠A = 107.9°, ∠B = 29°, ∠C = 43.1°, b = 22, c = 31

Use sin107.9°/a = sin29°/22 to find side a.

Second triangle: ∠A = 14.1°, ∠B = 29°, ∠C = 136.9°, b = 22, c = 31

Use sin14.1°/a = sin29°/22 to find side a.

Answer 3

sin29°/22 = sinC/31; sinC = 31sin29°/22 = 0,683141; C₁ = sin^-1(0.683141) = 43°; C₂ = 180° - 43° = 137°;

A₁ = 180°- (29° + 43°) = 108°; A₂ = 180° - (29° + 137°) = 14°

a₁/sin108° = 22/sin29°; a₁ = 22sin108°/sin29° = 43; a₂ = 22sin14°/sin29° = 11