Solve the triangle using the Law of Sines: Did I do this correctly?

Question

Given: <B = 29 degrees. <C = 51 degrees. b = 44

 

51 + 29 = 80 degrees. <A = 100 degrees.

 

Sin51° / c = sin29°/44

 

c = 44sin51° / sin29°

 

c = 70.5

 

then 

 

sin100° / a = sin29° / 44

 

a = 44sin100° / sin29°

 

a = 89.4

Answer 1

Well, you set it up correctly, but  c = 44*(sin(51^o)/sin(29⁰)) = 70.5, not 16.3.  Looks like you just computed c incorrectly. Your answer for a is correct.

 

The Triangle Inequality Theorem states that the smallest side will be opposite the smallest angle.  Since  angle B = 21^o is the smallest angle, side b = 44 must be the smallest side.  So getting an answer of 16.3 for a side opposite a larger angle should set off alarm bells in your head that you made a mistake.