show the work to solve the oblique triangles where A120 degr

show the work to solve the oblique triangle(s) where A=120 degrees, b=6, and c=7. Indicate the number of triangles. Round off all final two decimal places.Put \"N/A\" on an answer line to indicate no answer. B1=. B2=. C1=, C2=, a1=, a2=. PLEASE answer all of the above. Upper case letters are angle measures and lower case letters are sides of the triangle(s)

Solution

A=120 degrees, b=6, and c=7

Apply cosine Rule to find side a :

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

=6^2 +7^2 -2*6*7cos120

= 127

a = 11.27

Apply sine rule :

a/sinA = b/sinB

11.27/sin120 = 6/sinB

sinB = 0.461 ; B1 = 27.45 deg

B2 = 180 - B1 = 152.54 deg

C1 = 180 - A - B1 = 32.55 deg

C2 = 180 -120 - 152.54 = not possible

So, only one triangle possible with a = 11.27 , B =27.45 , C = 32.55 deg