1. Find Side a using Side b=7, Side c=8, Angle A=60 (Law of Cosines)

Solution:
We have `b=7,c=8,A=60`

The law of cosines states that
`a^2=b^2+c^2-2 b c * cos(A)`

`:.a^2=7^2+8^2-2*7*8*cos(60)`

`:.a^2=49+64-2*7*8*0.5`

`:.a^2=49+64-56`

`:.a^2=57`

`:.a=sqrt(57)`

`:.a=7.5498`

Perimeter `P=b+c+a=7+8+7.5498=22.5498`

Area `=1/2 bc*sin(A)=1/2 *7*8*sin(60)=1/2 *7*8*0.866=24.2487`