Answer:
[tex]EF=7.6\ units[/tex]
[tex]EG=15.9\ units[/tex]
[tex]m<G=28.6\°[/tex]
Step-by-step explanation:
step 1
Find the measure of side EF
we know that
In the right triangle EFG
[tex]tan(61.4\°)=\frac{FG}{EF}[/tex]
[tex]EF=\frac{FG}{tan(61.4\°)}[/tex]
[tex]EF=\frac{14}{tan(61.4\°)}[/tex]
[tex]EF=7.6\ units[/tex]
step 2
Find the measure of side EG
we know that
In the right triangle EFG
[tex]sin(61.4\°)=\frac{FG}{EG}[/tex]
[tex]EG=\frac{FG}{sin(61.4\°)}[/tex]
[tex]EG=\frac{14}{sin(61.4\°)}[/tex]
[tex]EG=15.9\ units[/tex]
step 3
Find the measure of angle G
wee know that
[tex]m>E+m<G=90\°[/tex] -----> by complementary angles
we have
[tex]m<E=61.4\°[/tex]
substitute
[tex]61.4\°+m<G=90\°[/tex]
[tex]m<G=90\°-61.4\°=28.6\°[/tex]
