use law of sines or cosines 17 40 20 125 Solutionby law ow s

use law of sines or cosines

17. 40 20 125;

by law ow sines

a/sinA =b/sinB=c/sinc

A =125^O ,a=40 , b =x ,c=20

let B=P

A+B+C =180^O

C =180^O-A-B

C =180^O-125^O-P

C =55^O-P

a/sinA =b/sinB=c/sinc

40/sin125^O =x/sinP=20/sin(55^O-P)

40/sin125^O =20/sin(55^O-P)

sin(55^O-P)=(20/40)sin125^O

sin(55^O-P)=0.409576

(55^O-P)=24.18^O

P=55^O-24.18^O

P=30.82^O

a/sinA =b/sinB

40/sin125^O =x/sinP

40/sin125^O =x/sin30.82^O

x=40(sin30.82^O/sin125^O)

x=40*0.62549

x=25