Show the work to solve the oblique triangles where A1024 deg

Show the work to solve the oblique triangle(s) where A=102.4 degrees, C=16.7 degrees, and a=21.6. Indicate the number of triangles. Round off all final answers to two decimal places. Put \"N/A\" on an answer line to indicate no answer. B1=, B2=, b1=, b2=, c1=, c2=. PLEASE answer all of the above. Capital letters are the degree measures and lower case letters are the side lengths of the triangle(s).

Solution

A=102.4 degrees, C=16.7 degrees, and a=21.6

B = 180 -A - C = 60.9 deg

Use sine rule to find remaining sides:

a/sinA = c/sinC

c = 21.6*sin16.7/sin102.4 = 6.35

a/sinA = b/sinB

b = 21.6*sin60.9/sin102.4

= 19.32