Answer: Option 'D' is correct.
Step-by-step explanation:
1) In Δ FGH,
FH=7 ft, FG=12 ft,
∠F=70 degrees
By "Law of cosines":
[tex]\cos F=\frac{12^2+7^2-GH^2}{2\times 12\times 7}\\\\\cos 70^\circ=\frac{144+49-GH^2}{168}\\\\\cos 70^\circ\times 168=193-GH^2\\\\57.45=193-GH^2\\\\135.54=GH^2\\\\GH=11.6\ ft[/tex]
So,By applying Law of Sines , we get that
[tex]\frac{\sin F}{11.6}=\frac{\sin G}{7}\\\\\frac{\sin 70^\cir}{11.6}=\frac{\sin G}{7}\\\\G=34.5^\circ[/tex]
Hence, Option 'D' is correct.
2) In Δ XYZ,
XY=14, ∠Y=22°, and XZ=26
By using "Law of sines":
[tex]\frac{\sin Y}{26}=\frac{\sin Z}{14}\\\\\frac{\sin 22^\circ}{26}=\frac{\sin Z}{14}\\\\Z=11.6^\circ[/tex]
so, X = 147° , Y = 22° , Z = 11.6°
