Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side a
To find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]
From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex]
[tex] |a| \sin(58) = 6\sin(109) [/tex]
Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]
a = 6.728791
a = 6.7 to the nearest tenth
For side c
To find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]
C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex]
[tex] |c| \sin(58) = 6 \sin(13) [/tex]
Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]
c = 1.591544
c = 2.0 to the nearest tenth
Hope this helps you
