Answer:
Part 1) [tex]FG=4.4\ units[/tex]
Part 2) [tex]EF=3.9\ units[/tex]
Part 3) [tex]m\angle G=63^o[/tex]
Step-by-step explanation:
step 1
Find the measure of length side FG
In the right triangle EFG
we know that
[tex]sin(27^o)=\frac{GE}{FG}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
substitute the given values
[tex]sin(27^o)=\frac{2}{FG}[/tex]
[tex]FG=\frac{2}{sin(27^o)}=4.4\ units[/tex]
step 2
Find the measure of length side EF
In the right triangle EFG
we know that
[tex]cos(27^o)=\frac{EF}{FG}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(27^o)=\frac{EF}{4.4}[/tex]
[tex]EF=cos(27^o)(4.4)=3.9\ units[/tex]
step 3
Find the measure of angle G
we know that
[tex]m\angle G+27^o=90^o[/tex] ---> by complementary angles in a right triangle
[tex]m\angle G=90^o-27^o=63^o[/tex]
