Answer:
[tex]AC=9.2[/tex]
Step-by-step explanation:
The Law of Sines states:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
The lower case letters represent the sides opposite the angles: ∠A - side a, ∠B- side b, ∠C- side c. It helps to make a model.
To Find AC, or side b, we can use A and B because we have the appropriate information to solve for b. Insert values:
[tex]\frac{sinA}{a}=\frac{sinB}{b} \\\\\frac{sin31}{5}=\frac{sin108}{b}[/tex]
Solve for b. Multiply both sides by b:
[tex]b*(\frac{sin31}{5})=b*(\frac{sin108}{b})\\\\b*\frac{sin31}{5} =sin108[/tex]
Multiply both sides by 5:
[tex]5*(b*\frac{sin31}{5} )=5*(sin108)\\\\b*sin31=5*sin108[/tex]
Divide both sides by sin 31:
[tex]\frac{b*sin31}{sin31} =\frac{5*sin108}{sin31} \\\\b=\frac{5*sin108}{sin31}[/tex]
Enter the simplified equation into a calculator:
[tex]b=9.2[/tex]
The length of AC is 9.2 units.
:Done
