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

- anonymous

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- chestercat

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- anonymous

@wolf1728 @Astrophysics

- wolf1728

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

- anonymous

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## More answers

- anonymous

yay and did I do that correctly?

- wolf1728

I guess you did (and good diagram)

- anonymous

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

- wolf1728

Yes you did!!

- wolf1728

Where's Astro?

- anonymous

@Astrophysics

- anonymous

not sure

- anonymous

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

- anonymous

you guys there?

- wolf1728

Two sides and included angle, we use Law of Cosines

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- Astrophysics

This should not be a right triangle

- Astrophysics

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

- wolf1728

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

- Astrophysics

You can use the sine law

- anonymous

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

- Astrophysics

That would be a whole lot easier

- anonymous

that is what wolf included correct

- Astrophysics

Not quite, he is using cosine law

- Astrophysics

But, I will let wolf continue :)

- anonymous

does it matter which one is used or?

- 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

- anonymous

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

- anonymous

hold on im looking

- wolf1728

How about 11.642 ?

- anonymous

how did you get that

- anonymous

its one of the answers but I am trying to learn

- Astrophysics

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

- Astrophysics

Oh I guess wolf already did it xD

- anonymous

Ok I was just a little off on the graph

- 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.

- Astrophysics

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

- wolf1728

was 11.642 an answer?

- anonymous

11.6 yes

- wolf1728

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

- Astrophysics

Alright cool! :)

- Astrophysics

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

- anonymous

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

- anonymous

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

- wolf1728

all right !!

- anonymous

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

- anonymous

|dw:1433835840125:dw|

- anonymous

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

- wolf1728

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

- anonymous

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

- wolf1728

Using side angle side formula I get 26.997

- 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

- wolf1728

You were using the formula?

- anonymous

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

- wolf1728

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

- anonymous

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

- wolf1728

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

- anonymous

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

- wolf1728

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

- anonymous

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

- anonymous

have to simplify it

- anonymous

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

- wolf1728

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

- anonymous

can you help?

- anonymous

I have answer choices if its easier

- wolf1728

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

- anonymous

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

- wolf1728

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

- anonymous

theres no triangle its just says to simplify the trigonomic equation

- anonymous

im looking up trig identies

- wolf1728

Okay and I made a quick graphic

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- anonymous

\[http://www.math.com/tables/trig/identities.htm would this help\]

- 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)

- anonymous

does it help?

- wolf1728

Yes I think I found something

- anonymous

where at

- anonymous

I might have found something too

- 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))

- anonymous

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

- 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))

- wolf1728

Hmmm now to simplify that

- anonymous

which seems tricky

- anonymous

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

- 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))

- anonymous

theres a discrepancy here somewhere

- 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

- anonymous

whats your name btw?

- 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

- anonymous

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

- 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.

- anonymous

lol maybe our brains are fried!

- wolf1728

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

- anonymous

roughly yes lol...are you tired?

- wolf1728

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

- wolf1728

whoops - just got "bumped" from openstudy

- anonymous

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

- anonymous

what does that mean

- wolf1728

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

- wolf1728

"bumped" means getting tossed off openstudy

- anonymous

oh im sorry i hope it wasnt my fault

- wolf1728

no - sometimes it just happens

- anonymous

sweetie pies daughter

- anonymous

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

- wolf1728

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

- anonymous

:)

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