Answer: The perimeter is 32.31
Step-by-step explanation:
1. You can use the Sines Law, as following:
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}[/tex]
2. The sum of the interior angles of a triangle is 180°, therefore, you can calculate the angle B:
[tex]B=180-45-60=75[/tex]°
3. Let's find BC:
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}\\\frac{9}{sin(45)}=\frac{BC}{sin(60)}\\BC=\frac{9sin(60)}{sin(45)}\\BC=11.02[/tex]
4. Now, calculate AC:
[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}\\\frac{9}{sin(45)}=\frac{AC}{sin(75)}\\AC=\frac{9sin(75)}{sin(45)}\\AC=12.29[/tex]
5. Therefore, the perimeter is:
[tex]P=AB+AC+BC\\P=9+12.29+11.02\\P=32.31[/tex]
