Solve the triangle The Law of Cosines may be needed Standard

Solve the triangle. The Law of Cosines may be needed. (Standard notation for triangle ABC is used throughout. Round your answer to two decimal places. If no such triangle exists, enter \'NONE\' in each of the answer blanks.)

b = 18.4, c = 4.4, B = 36.1°

Solution

law of sine is

a/sinA =b/sinB =c/sinC

we know b and c

so b/sinB =c/sinC

18.4/sin36.1 = 4.4/sinC

sinC = 4.4 *0.59 /18.4

sinC = 2.596/18.4

SinC=0.141

C= 8.1

we know A+B+C=180

A+36.1 +8.1 =180

A= 136 degree 58\'

a/sin136.58 = 18.4/sin36.1

a = 18.4*0.69/0.59

a= 21.52