Pre- Calc Law of Sins equation

Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.) 

b = 28, c = 31, ∠B = 24°

∠A₁ =

 ∠A₂ =

∠C₁ =

 ∠C₂ =

 a₁₌    a2=

Answer 1

Sine Law: c/sinC = b/sinB; sinC = csinB/b = 31sin24°/28; C₂ = sin^-1(31sin24°/28) = 26.8°; C₁ = 180° - 26.8° =

153.2°; Now A₁ = 180°- (24° + 153.2°) = 2.8°; A₂ = 180° - (24° + 26.8°) = 129.2°;

a₁/sinA₁ = b/sinB; a₁ = bsinA₁/sinB = 28sin2.8°/sin24° = 3.4; the same way a₂ = bsinA₂/sinB = = =28sin129.2°/sin24° = 53.4

Answer 2

Angle A on the top, angle C on the left, angle B on the right

and A is the largest (obtuse) angle

side b = AC = 28

side c = AB = 31

angle B = 28

sin 24 / 28 = sin C / 31

sin 24 * 31 / 28 = sin C

0.45031556911963594429905591787809 = sin C

taking the inverse_sine or arcsin...

angle C = 26.763932338912905561513628765426

The obtuse angle is 125.23606766108709443848637123457

sin A/a = sin 24/28

sin A * 28 / sin 24 = a

a = 56.227765122947388633485437692347