Answer:
[tex]c=13.8\ units[/tex]
Step-by-step explanation:
step 1
Find the measure of angle B
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]
substitute the given values and solve for sin(B)
[tex]\frac{8}{sin(35\°)}=\frac{10}{sin(B)}[/tex]
[tex]sin(B)=sin(35\°)(10)/8[/tex]
[tex]B=arcsin(sin(35\°)(10)/8)[/tex]
[tex]B=45.8\°[/tex]
step 2
Find the measure of angle C
Remember that
The sum of the interior angles of a triangle must be equal to 180 degrees
so
[tex]A+B+C=180\°[/tex]
substitute and solve for C
[tex]35\°+45.8\°+C=180\°[/tex]
[tex]80.8\°+C=180\°[/tex]
[tex]C=180\°-80.8\°=99.2\°[/tex]
step 3
Find the measure of side c
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]
[tex]\frac{8}{sin(35\°)}=\frac{c}{sin(99.2\°)}[/tex]
[tex]c=\frac{8}{sin(35\°)}(sin(99.2\°))}[/tex]
[tex]c=13.8\ units[/tex]
