Answer:
Part 1) The measure of angle A is [tex]A=80\°[/tex]
Part 2) The length side of a is equal to [tex]a=10.9\ units[/tex]
Part 3) The length side of b is equal to [tex]b=6.3\ units[/tex]
Step-by-step explanation:
step 1
Find the measure of angle A
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
[tex]A+B+C=180\°[/tex]
substitute the given values
[tex]A+35\°+65\°=180\°[/tex]
[tex]A+100\°=180\°[/tex]
[tex]A=180\°-100\°=80\°[/tex]
step 2
Find the length of side a
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]
substitute the given values
[tex]\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}[/tex]
[tex]a=\frac{10}{sin(65\°)}(sin(80\°))[/tex]
[tex]a=10.9\ units[/tex]
step 3
Find the length of side b
Applying the law of sines
[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
substitute the given values
[tex]\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}[/tex]
[tex]b=\frac{10}{sin(65\°)}(sin(35\°))[/tex]
[tex]b=6.3\ units[/tex]
