## anonymous one year ago In triangle FGH, FH=7feet FG=12feet and measurement F=70 degrees. Find measurement G round to the nearest tenth

1. anonymous

@wolf1728 @Astrophysics

2. wolf1728

Hello !!! I got "bumped" and I entered this topic!!!

3. anonymous

|dw:1433834150459:dw|

4. anonymous

yay and did I do that correctly?

5. wolf1728

I guess you did (and good diagram)

6. anonymous

Thats what I meant *did i do the diagram correctly*

7. wolf1728

Yes you did!!

8. wolf1728

Where's Astro?

9. anonymous

@Astrophysics

10. anonymous

not sure

11. anonymous

can you help me get it started and i do it and you tell me if im doing it wrong or not

12. anonymous

you guys there?

13. wolf1728

Two sides and included angle, we use Law of Cosines

14. Astrophysics

This should not be a right triangle

15. Astrophysics

Otherwise we could just say it's 20 degrees ;)

16. wolf1728

b=7 c =12 Angle A=70 degrees a^2 = (b^2 + c^2) -(2*b*c * cos(A))

17. Astrophysics

You can use the sine law

18. anonymous

So one side should be longer...i was thinking the same! but 20 isnt a answer choice!

19. Astrophysics

That would be a whole lot easier

20. anonymous

that is what wolf included correct

21. Astrophysics

Not quite, he is using cosine law

22. Astrophysics

But, I will let wolf continue :)

23. anonymous

does it matter which one is used or?

24. wolf1728

a^2 = 7^2 + 12^2 -(2*7*12*cos(70) a^2 = 49 + 144 - (108*.34202) a^2 = 193 -36.93816 a^2 = 156.06184 a = sq root(156.06184) a = 12.49

25. anonymous

I dont think thats correct its not a choice I have maybe we have to use Cos*b*

26. anonymous

hold on im looking

27. wolf1728

How about 11.642 ?

28. anonymous

how did you get that

29. anonymous

its one of the answers but I am trying to learn

30. Astrophysics

Well lets redraw the triangle and put everything in place, and continue from there |dw:1433835265958:dw|

31. Astrophysics

Oh I guess wolf already did it xD

32. anonymous

Ok I was just a little off on the graph

33. wolf1728

a^2 = 49 + 144 - (168*.34202) a^2 = 193 - (57.45936) a^2=135.54064 a = 11.6421922334 ARRGGGHHHH !!!!!!!!!!! The other time I made an arithmetic mistake.

34. Astrophysics

I try not to make right triangles, but always end up doing so haha, and good job wolf I believe in you! :P

35. wolf1728

was 11.642 an answer?

36. anonymous

11.6 yes

37. wolf1728

all right !!!!!!!!!!!!!!!!

38. Astrophysics

Alright cool! :)

39. Astrophysics

Did you understand everything, sorry about the first question it was a bit messy, I'll go look at it again later...

40. anonymous

wait dont go anywhere I am gonna show you the work for a problem and I just would like for you to check

41. anonymous

slowly but surely I know a lot more than I did before I came here

42. wolf1728

all right !!

43. anonymous

Okay so Im finding the area of a triangle and it looks like

44. anonymous

|dw:1433835840125:dw|

45. anonymous

so I did 12^2-7^2=b and got 144-49=95

46. wolf1728

There is a side angle side formula for triangle area Area = (1/2) * side 1 * sine (included angle) * side 2

47. anonymous

then i did sin*40*95 and got 61.6 and divided it by 2 and got 30.53

48. wolf1728

Using side angle side formula I get 26.997

49. anonymous

that was my second choice, when my calculator was on rads i got a different answer than I did when it was on degrees I just didn't know which I should have been on

50. wolf1728

You were using the formula?

51. anonymous

I had seen another question similar to this and I was following along but with my question instead

52. wolf1728

You can find a side angle side triangle area calculator here http://www.1728.org/triang.htm (It's my own website)

53. anonymous

Really???!!! thats so cool! I'm gonna check it out! and If you dont mind checking 2 more questions with me

54. wolf1728

Wow - two more?? Well I'll try - go ahead

55. anonymous

im sorry I just want to understand it and the calculator isnt working....ill add more to your testimonial

56. wolf1728

okay - by the way my site has got about 250 pages I'd say half the pages are all kinds of calculators

57. anonymous

$\sin ^{2} \Theta \over 1- \cos \theta$

58. anonymous

have to simplify it

59. anonymous

I am going to keep that site itll help me a lot

60. wolf1728

Hmmmm that's probably a trigonometric identity. (I'm glad you like my site).

61. anonymous

can you help?

62. anonymous

I have answer choices if its easier

63. wolf1728

I was just doing a web search for trig identities. Maybe I can solve it myself.

64. anonymous

I belive you can youve been doing great i feel im in comfortable hands

65. wolf1728

sine(angle) = y/hypotenuse cosine = x/hyp

66. anonymous

theres no triangle its just says to simplify the trigonomic equation

67. anonymous

im looking up trig identies

68. wolf1728

Okay and I made a quick graphic

69. anonymous

$http://www.math.com/tables/trig/identities.htm would this help$

70. wolf1728

okay let me see that page in the meantime, I started with this sine^2 = (y^2 / hyp^2) 1 - cos = (1 -x/hyp)

71. anonymous

does it help?

72. wolf1728

Yes I think I found something

73. anonymous

where at

74. anonymous

I might have found something too

75. wolf1728

Almost at the top of the page they state: sin^2(x) + cos^2(x) = 1 and you have to simplify sin^2(Θ) / (1−cos(θ))

76. anonymous

like this sin^2 (a) * (1 + cos(a)) / (1 - cos^2 (a)) = 1 + cos(a

77. wolf1728

sin^2(x) + cos^2(x) = 1 Therefore, sin^2(x) = 1 -cos^2(x) SO, we can say sin^2(Θ) / (1−cos(θ)) equals (1 -cos^2(x)) / (1 - cos(x))

78. wolf1728

Hmmm now to simplify that

79. anonymous

which seems tricky

80. anonymous

the -cos 2 and the cos would leave one -cos right?

81. wolf1728

I don't know - that would be considered "cancelling terms" which should NOT be done. I got: (1 -cos^2(x)) / (1 - cos(x)) = (1 - (cos(x) * cos(x))) / (1 -cos(x))

82. anonymous

theres a discrepancy here somewhere

83. anonymous

Ill keep looking at it and I will message you if there was something wrong with the question...youve helped me a lot I dont want you to feel like im over doing it

84. anonymous

whats your name btw?

85. wolf1728

I'm thinking of trying one more thing - actuallly calculating values of sine and cosine My name is Robert - but wolf is okay too

86. anonymous

Mucho Gusto! and how are you going to do that? im summer and sorry my computer froze up

87. wolf1728

Okay I looked up sine 35 degrees 0.57358 squaring that we get 0.3289940164 cosine 35 degrees = 0.81915 1 minus that = 0.18085 sine 45 degrees 0.70711 squaring that 0.5000045521 cosine 45 degrees 0.70711 1 minus that = 0.29289 Well, that doesn't show much does it? Maybe it's time to quit.

88. anonymous

lol maybe our brains are fried!

89. wolf1728

Yes, we've been doing this stuff for about 2 hours?

90. anonymous

roughly yes lol...are you tired?

91. wolf1728

Yes I am tired - think I'll call it a night.

92. wolf1728

whoops - just got "bumped" from openstudy

93. anonymous

Alright goodnight and ill let my mom know you helped me im sure shell do a better testimonial

94. anonymous

what does that mean

95. wolf1728

that's okay - and thanks. Might as well get going. It was good meeting you SweetiePie

96. wolf1728

"bumped" means getting tossed off openstudy

97. anonymous

oh im sorry i hope it wasnt my fault

98. wolf1728

no - sometimes it just happens

99. anonymous

sweetie pies daughter

100. anonymous

welll im gonna let you go i really appreciate all the help night

101. wolf1728

Thank you and I was glad to help - see you later

102. anonymous

:)