Solve the triangles if possible to do so and tabulate the un

Solve the triangles (if possible to do so) and tabulate the unknown parameters ONLY. a) A = 40degree, a= 3 and b = 2. b) a = 4, b = 3, and c = 6 c) a = 2, b = 3, and C = 60 degree.

Solution

a) A = 40 deg ; a= 3 ; b =2

use sine rule:

a/sinA = b/sinB

3/sin40 = 2/sinB

sinB = 2*sin40 /3 = 0.4285 =

B = 25.37 deg

C = 180 - B - C = 180 - 40 - 25.37 = 154.63 deg

a/sinA = c/sinC

c = a*sinC/sinA = 2.0

b) a = 4 . b = 3 and c =6

Apply cosine rule:

c^2 = a^2 +b^2 - 2abcosC

cosC = (4^2 +3^2 - 6^2)/2*4*3

= -0.3583

C = 117.28 deg

apply sine rule to find angle A

a/sinA = c/sinC

sinA = a*sinC/c = 2*sin117.28/6

= 0.296

A = 17.23

C = 180 - A - B = 45.49 deg

c) a =2 ; b =3 and C = 60 deg

apply cosine rule:

c^2 = a^2 +b^2 - 2abcosC

= 2^2 + 3^2 - 2*2*3cos60

= 7

c = 2.64

apply sine rule to find angle A

a/sinA = c/sinC

sinA = 2*sin60/2.64 = 0.656

A = 41 deg

B = 180 -A - C = 180 -41 -60 = 79 deg