Trigonometry of Angles

Question

Solve triangle ABC. (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 = 122,    c = 161,    ∠B = 42°

Find Angle A1

Angle A2

Angle C1

Angle C2

a1 =

a2 =

Answer 1

Set up the following equation using the law of sines:

sin 42/122 = sin c/161

sin c = 161(sin 42)/122

sin c = -1.209

If you try to solve this, the calculator gives you an error. This is because the domain of sin is [-1,1], this is outside the domain. Therefore, there is DNE.