Answer:
PK= 8.5
Step-by-step explanation:
The sum of interior angles in a triangle is 180 degree
[tex]m<k+m<p+m<s=180[/tex]
[tex]m<k+105+30=180[/tex]
[tex]m<k+135=180[/tex]
Subtract 135 from both sides
[tex]m<k=45[/tex]
Now use sine rule
[tex]\frac{sin A}{a} =\frac{sin B}{b}[/tex]
[tex]\frac{sin K}{PS} =\frac{sin S}{PK}[/tex]
[tex]\frac{sin(45)}{12} =\frac{sin(30)}{PK}[/tex]
Cross multiply
[tex]PKsin(45)}=12sin(30)[/tex]
[tex]PK =\frac{12sin(30)}{sin(45)}[/tex]
PK= 8.5
