Answer:
10). m∠x = 47°
11). x = 30.96
Step-by-step explanation:
10). By applying Sine rule in the given triangle DEF,
[tex]\frac{\text{SinF}}{\text{DE}}=\frac{\text{SinD}}{\text{EF}}[/tex]
[tex]\frac{\text{Sinx}}{7}=\frac{\text{Sin110}}{9}[/tex]
Sin(x) = [tex]\frac{7\times (\text{Sin110})}{9}[/tex]
Sin(x) = 0.7309
m∠x = [tex]\text{Sin}^{-1}(0.7309)[/tex]
m∠x = 46.96°
m∠x ≈ 47°
11). By applying Sine rule in ΔRST,
[tex]\frac{\text{SinR}}{\text{ST}}=\frac{\text{SinT}}{\text{RS}}[/tex]
[tex]\frac{\text{Sin120}}{35}=\frac{\text{Sin50}}{x}[/tex]
x = [tex]\frac{35\times (\text{Sin50})}{\text{Sin120}}[/tex]
x = 30.96
