Sin A = OPP/HYP

sin A /1 = h/c
h=c sin A

1) A=60" B=40" c=6

60" + 40" = 100"
180" - 100" = 80"
C= 80"

we find angle a

a/sin A = c/sin C
a/sin 60" = 6/sin 80"
a sin 80" = 6 sin 60"/ sin 80"
a= 5.2/ 0.98
a= 5.31

we find angle b

b/ sin B = c/ sin C
b/ sin 40" = 6/ sin 80"
b sin 80" = 6 sin 40" / sin 80"
b= 3.86 / 0.98
b= 3.94
LAW OF COSINES

a^2 = b^2 + c^2 - 2bc cos A
b^2= a^2 + c^2 -2bc cos B
c^2= a^2 + b^2 -2bc cos C

1) a=45 b=67 C=35"

c^2= (45)^2 + (67)^2 -2(45)(67) cos 35"
= 2025 + 4487 + - 6030 (0.8192)
c^2[squareroot]= [squareroot]1574
c= 39.67 or 39.7

c/ sin C = a/ sin A
39.7/ sin 35" = 45/ sin A
sin A= 45 sin 35"/ 39.7
sin A = 25.81/ 39.7
A= 0.65 (sin-^1)
A= 40'"54'
A= 40"32'

B= 180" - (40"32' +85")
B= 75"32