STEP - BY - STEP EXPLANATION
What to find?
g, E and e
Given:
Step 1
Find the measure of side g using the sine ratio.
[tex]\begin{gathered} \frac{sinF}{f}=\frac{sinG}{g} \\ \\ \frac{sin27.3}{17.78}=\frac{sin102.1}{g} \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=\frac{17.78sin102.1}{sin27.3} \\ \\ g\approx37.9 \end{gathered}[/tex]
Step 2
Find angle E.
[tex]E+F+G=180(sum\text{ of interior angle in a triangle\rparen}[/tex][tex]\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}[/tex]
Step 3
Find side e using the sine ratio.
[tex]\begin{gathered} \frac{sinE}{e}=\frac{sinF}{f} \\ \\ \frac{sin50.6}{e}=\frac{sin27.3}{17.78} \\ \\ esin27.3=17.78sin50.6 \\ \\ e=\frac{17.78sin50.6}{sin27.3} \\ \\ e\approx29.96 \end{gathered}[/tex]
ANSWER
g=37.9
E=50.6°
e = 29.96
