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 = 124, c = 162, ∠B = 44°

Question

<A1? <A2?

<C1? <C2?

a1? <a2?

Answer 1

I recommend to use the Law of Sines

c/b = sin(C)/sin(B)

From that we can calculate

sin(C) = sin(B)c/b

C = arcsin(sin(B)c/b)

Substituting actual values

C1 = arcsin(sin(44°)×162/124) = 64.2°

C2 = 180° - C1 = 115.8°

Calculate the angle A from

A = 180° - B - C

A1 = 180° - 44° - 64.2° = 71.8°

A2 = 180° - 44 - 115.8° = 20.2°

Calculate a from the Law of Sines

a = b×sin(A)/sin(B)

a1 = 124 × sin(71.8°) / sin(44°) = 169.6

a2 = 124 × sin(20.2°) / sin(44°) = 61.6