Use the Law of Sines to solve for all possible triangles tha

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.) a = 27, c = 18, C = 29°

Solution

Using sine law

sin C/c=sinA₁/a

sin 29/18=sin A₁/27

sinA₁=27sin 29/18

A₁=46.7degree

A₂=180-46.7= 133.3 degree

B₁=180-C-A₁=104.3 degree

And B₂=180-C-A₂=17.7degree

sin B₁/b=sinC/c

sin 104.3/b₁=sin 29/18

b₁=18sin 104.3/sin 29=36

b2=18 sin 17.7/sin 29=11.3