Question

In triangle FGH, FH = 8 ft, FG = 13 ft, and m F = 72°. Find m G. Round your answer to the nearest tenth.

Answer 1

Other person is correct. here are the summarized answer for my unit test right triangles and trigonometry unit test

1. side lengths 24, 32, and 40

right

2. a is right angle m b = 45

14\/2

3.quilt squares hypotenuse 18

9\/2

4.what are the values of the variables in the triangle below y, x, 30 degrees, 12\/3

x=18 y=6\/3

5.cos_=9/5

63.26

6. victor drives 300 meters up hill

292.3

7. the students in Mr. Collins class 59 degrees 63 feet

105 feet

8. an airplane pilot 5172 meters

912

9. to find the height of a pole 140 feet away 4 feet tall 44 degrees

139 feet

10. art piece 21in

191.0

11. a grid shows the positions of a subway (-7,-1) (-3,4)

6

12. triangle def m d 44 m d 61 ef 20 in

27.8

13.measure of j 16 103 degrees 11

42

14. triangle fgh fh 8 fg 13 m f 72 degrees

35.9

15. in triangle xyz xy 13 yz 20 xz 25

31

Won't do written part.

Explanation:

Answer 2

35.9°

Explanation:

The triangle is shown below.

Using cosine rule for the triangle ΔFGH,

`(GH)^(2)=(FG)^(2)+(FH)^(2)-2(FG)(FH)cos(\angle F)`

`(GH)=\sqrt{((FG)^(2)+(FH)^(2)-2(FG)(FH)cos(\angle F))}`

Plug in 8 ft for FH, 3 ft for FG and 72° for ∠F. Solve for GH.

⇒
`(GH)=\sqrt{(13)^(2)+(8)^(2)-2(13)(8)cos(72)}=12.99\textrm{ ft}`

Now, we use sin rule and evaluate ∠G.

Sine rule is given as,

`(sin(\angle G))/(FH)=(sin(\angle F))/(GH)`

Plug in 8 ft for FH, 12.99 ft for GH and 72° for ∠F. Solve for ∠G.

This gives,

`(sin(\angle G))/(FH)=(sin(\angle F))/(GH)\\(sin(\angle G))/(8)=(sin(72))/(12.99)\\sin(\angle G)=(sin(72))/(12.99)* 8 \\\\sin(\angle G)=0.5857\\\\\angle G=sin^(-1)(0.5857)\\ \angle G=35.9`

∴
`\angle G=35.9`°

Therefore, the measure of angle G is 35.9°