Answer:
The answer is below
Step-by-step explanation:
Given the triangle with: A = 32°, a = 19, b = 14
The sine rule states that for a triangle with lengths of a, b and c and the corresponding angles which are opposite the sides as A, B and C, then the following rule holds:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Given, that for triangle ABC; A = 32°, a = 19, b = 14. therefore:
[tex]\frac{a}{sinA}=\frac{b}{sinB}\\\\\frac{19}{sin(32)}=\frac{14}{sin(B)}\\\\sin(B)=\frac{14*sin(32)}{19} \\\\sin(B)=0.39\\\\B=sin^{-1}(0.39)\\\\B=23^o[/tex]
A + B + C = 180° (sum of angles in a triangle)
32 + 23 + C = 180
55 + C = 180
C = 180 - 55
C = 125°
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}\\\\\frac{19}{sin(32)}=\frac{c}{sin(125)} \\\\c=\frac{19*sin(125)}{sin(32)} \\\\c=29.4[/tex]
