1. Find Side a using Side b=3, Angle A=60, Angle B=45 (Law of Sines)

Solution:
The law of sines states that
`a/sin(A)=b/sin(B)=c/sin(C)`

We have `b=3,A=60,B=45`

`:.a/sin(A)=b/sin(B)`

`:.a=(b*sin(A))/sin(B)`

`:.a=(3*sin(60))/sin(45)`

`:.a=(3*0.866)/(0.7071)`

`:.a=3.6742`

`A+B+C=180`

`:.C=180-(A+B)`

`:.C=180-(60+45)`

`:.C=180-105`

`:.C=75`

`c/sin(C)=b/sin(B)`

`:.c=(b*sin(C))/sin(B)`

`:.c=(3*sin(75))/sin(45)`

`:.c=(3*0.9659)/(0.7071)`

`:.c=4.0981`

perimeter `P=a+b+c=3.6742+3+4.0981=10.7723`

Area `=1/2 ab*sin(C)=1/2 *3.6742*3*sin(75)=1/2 *3.6742*3*0.9659=5.3236`