Question

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.

a. 17.3 degrees
b.11.6 degrees
c. 78 degrees
d. 34.4 degrees

2. In triangle XYZ, XY=14, Y=22, and XZ=26. What is the measure of angle Z to the nearest degree?
a. 57 degrees
b. 66 degrees
c. 147 degrees
d. 33 degrees

Answer 1

Hello there! :)

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

Answer 2

Answer: Option 'D' is correct.

Explanation:

1) In Δ FGH,

FH=7 ft, FG=12 ft,

∠F=70 degrees

By "Law of cosines":

`\cos F=(12^2+7^2-GH^2)/(2* 12* 7)\\\\\cos 70^\circ=(144+49-GH^2)/(168)\\\\\cos 70^\circ* 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

`(\sin F)/(11.6)=(\sin G)/(7)\\\\(\sin 70^\cir)/(11.6)=(\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":

`(\sin Y)/(26)=(\sin Z)/(14)\\\\(\sin 22^\circ)/(26)=(\sin Z)/(14)\\\\Z=11.6^\circ`

so, X = 147° , Y = 22° , Z = 11.6°