Use the Law of Sines

Question

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 = 28,    c = 39,    ∠B = 22°

Answer 1

sinC/c= sinB/b=sin22/28

sinC=39sin22/28

C=arcsin(39sin22/28)

C= about 31.45

or C= 180-31.45=148.55

then A=B-C=180-22-148.55= 9.45

A=180-C-B= 180-22-31.45= 126.55 or 9.45

A1=9.45, C1=148.55, B1=22, a1=12.27, c1=39, b1=28 for the acute triangle

A2=126.55, C2=31.45, B2=22, a2=60.05, c2=39, b2=28 for the obtuse triangle

a/sinA=b/sinB

a=bsinA/sinB=28sin9.45/sin22 or 28sin126.55/sin22= about 12.27 or 60.05