Question

How do I solve this problem?

Answer 1

`EF=7.6\ units`

`EG=15.9\ units`

`m<G=28.6\°`

Explanation:

step 1

Find the measure of side EF

we know that

In the right triangle EFG

`tan(61.4\°)=(FG)/(EF)`

`EF=(FG)/(tan(61.4\°))`

`EF=(14)/(tan(61.4\°))`

`EF=7.6\ units`

step 2

Find the measure of side EG

we know that

In the right triangle EFG

`sin(61.4\°)=(FG)/(EG)`

`EG=(FG)/(sin(61.4\°))`

`EG=(14)/(sin(61.4\°))`

`EG=15.9\ units`

step 3

Find the measure of angle G

wee know that

`m>E+m<G=90\°` -----> by complementary angles

we have

`m<E=61.4\°`

substitute

`61.4\°+m<G=90\°`

`m<G=90\°-61.4\°=28.6\°`