Answer:
b = 9.5 , c = 15
Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]
a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex]
[tex] |b| \sin(23) = 7 \sin(32) [/tex]
Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]
b = 9.493573
b = 9.5 to the nearest tenth
For c
To find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex]
[tex] |c| \sin(23) = 7 \sin(125) [/tex]
Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]
c = 14.67521
c = 15.0 to the nearest tenth
Hope this helps you
