a=sqrt(b^2+c^2-2bc*cos(A))
b=sqrt(a^2+c^2-2ac*cos(B))
c=sqrt(a^2+b^2-2ab*cos(C))
33.
given: A=24° , a=4, b=18
a=sqrt(b^2+c^2-2bc*cos(A))
4=sqrt(324+c^2-36c *cos(24°) )
16=324+c^2-36c *0.9135454576426
16=c^2-32.8877c +324
c=sqrt(4^2+18^2-2*4*18*cos(C))
c=sqrt(340 - 144cos(C))
c^2=340 - 144cos(C)
substitute in
16=(340 - 144cos(C))^2-32.8877sqrt(340 - 144cos(C)) +324
no real solution
35. A=42°, B=35°, c=1.2
C=180-(42+35)=103°
a=sqrt(b^2 - 1.78355 b + 1.44)
a^2=b^2 - 1.78355 b + 1.44
substitute in
b=sqrt(a^2+c^2-2ac*cos(B))
b=sqrt(b^2 - 1.78355 b + 1.44+1.2^2-2(b^2 - 1.78355 b + 1.44)*1.2*cos(35))
b=sqrt(-0.965965 b^2 + 1.72285 b + 0.0490105)
b^2=-0.965965 b^2 + 1.72285 b + 0.0490105
b^2+0.965965 b^2 - 1.72285 b - 0.0490105=0
b≈-0.028-> disregard negative solution for side
b=0.9
then
a^2=b^2 - 1.78355 b + 1.44
a^2=(0.904)^2 - 1.78355*0.904 + 1.44
a^2=0.6448868
a=sqrt(0.6448868)
a=0.8
use same way to solve 36
