In triangle FGH, FH=7 ft, FG=12 ft, and m(italic m) angle F=70 degrees. Find m(italic) angle G. Round your answer to the nearest tenth.

A17.3 degrees

b.11.6 degrees

C78 degrees
D34.4 degrees

In triangle XYZ, XY=14, Y=22, and XZ=26. What is the measure of angle Z to the nearest degree?

A57 degrees
B66 degrees
C147 degrees
D33 degrees

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1. In triangle FGH, FH=7 ft, FG=12 ft, and m(italic m) angle F=70 degrees. Find m(italic) angle G. Round your answer to the nearest tenth.

d. 34.4 degrees

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RenatoMattice RenatoMattice · Answer 2 · 2019-03-01T03:19:43-05:00

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":

\(\cos F=\frac{12^2+7^2-GH^2}{2\times 12\times 7}\\\\\cos 70^\circ=\frac{144+49-GH^2}{168}\\\\\cos 70^\circ\times 168=193-GH^2\\\\57.45=193-GH^2\\\\135.54=GH^2\\\\GH=11.6\ ft\)

So,By applying Law of Sines , we get that

\(\frac{\sin F}{11.6}=\frac{\sin G}{7}\\\\\frac{\sin 70^\cir}{11.6}=\frac{\sin G}{7}\\\\G=34.5^\circ\)

Hence, Option 'D' is correct.

2) In Δ XYZ,

XY=14, ∠Y=22°, and XZ=26

By using "Law of sines":

\(\frac{\sin Y}{26}=\frac{\sin Z}{14}\\\\\frac{\sin 22^\circ}{26}=\frac{\sin Z}{14}\\\\Z=11.6^\circ\)

so, X = 147° , Y = 22° , Z = 11.6°