Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 20, b = 42, c = 28

Question

Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.)

a = 20,    b = 42,    c = 28

Answer 1

B>C>A

B = 180-C-A

C= 180-B-A

A = 180-B-C

use the Law of Cosines first

c^2 = a^2 + b^2 -2abCosC

28^2= 20^2+42^2-2(20)(42)cosC

cosC= 1380/1680

C=arccos(138/168)

C=about 34.77 degrees

then use either sine or cosine law to find A and B

20^2=28^2+42^2-2(28)(42)cosA

A=about 24.04

B=180-24.04-34.77=121.19