Question

< = angles

determine how many solution exist

13 years ago

Answer 1

\[\frac{ a }{ \sin A }=\frac{ b }{ \sin B }\]
\[\frac{ 62 }{ \sin 54 }=\frac{ 75 }{ \sin B }\]
62 sin B = 75 sin 54
sin B = 0.9786
B = 78.1 or (180 - 78.1 = 101.9
there are 2 solutions:
Solution 1:
<B = 78.1 <C = 180 - 78.1 - 54 = 47.9
\[\frac{ a }{ \sin A }=\frac{ c }{ \sin C }\]
\[\frac{ 62 }{ \sin 54 }=\frac{ c }{ \sin 47.9 }\]
c sin 54 = 62 sin 47.9
c = 56.9
Solution 2:
<B = 101.9 <C = 180 - 101.9 - 54 = 24.1
\[\frac{ a }{ \sin A }=\frac{ c }{ \sin C }\]
\[\frac{ 62 }{ \sin 54 }=\frac{ c }{ \sin 24.1}\]
c sin 54 = 62 sin 24.1
c = 31.3