webassign 66 HmwkThe Law of Cosines Homework Solve triangle

webassign 6.6 Hmwk-The Law of Cosines (Homework)

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 thanA₂.)

b = 123,    c = 161,    B = 48°

A₁ =

°

A₂ =

°

C₁ =

°

C₂ =

°

a₁ =

a₂ =

Solution

by law of sines b/sinB =c/sinC

123/sin48 =161/sinC

sinC=(161/123)sin48

C₁=76.6^o,C₂=103.4^o

A₁+B+C₁=180 ,A₂+B+C₂=180

A₁+48+76.6=180,A₂+48+103.4=180

A₁=55.4^o,A₂=28.6^o

a₁/sinA₁=b/sinB

a₁/sin55.4=123/sin48

a₁=136.2

a₂/sinA₂=b/sinB

a₂/sin28.6=123/sin48

a₂=79.2